1082 lines
No EOL
42 KiB
HTML
1082 lines
No EOL
42 KiB
HTML
<!DOCTYPE HTML>
|
|
<HTML LANG="en-us"
|
|
><HEAD
|
|
><TITLE
|
|
>sinh, cosh, tanh, asinh, acosh, atanh | Common Lisp Nova Spec</TITLE
|
|
><META CHARSET="US-ASCII"
|
|
><LINK REL="canonical" HREF="f_sinh.html"
|
|
><LINK REL="next" HREF="f__star.html" TYPE="text/html" TITLE="*"
|
|
><LINK REL="prev" HREF="v_pi.html" TYPE="text/html" TITLE="pi"
|
|
><LINK REL="up" HREF="12_2_Numbers_Dictionary.html" TYPE="text/html" TITLE="12.2 Numbers Dictionary"
|
|
><LINK REL="start" HREF="index.html" TYPE="text/html" TITLE="Common Lisp Nova Spec"
|
|
><META NAME="VIEWPORT" CONTENT="width=device-width, initial-scale=1.0"
|
|
><LINK REL="STYLESHEET" HREF="dpans.css%3F3909942064.css"
|
|
><SCRIPT SRC="dpans.js%3F3909942064"
|
|
></SCRIPT
|
|
><SCRIPT SRC="apropos.js%3F3909942064"
|
|
></SCRIPT
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy7.ttf') }
|
|
@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmmi7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi7.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
#G24 { position:absolute;left:0.000pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G24:before {display:inline-block;content:'';height:10.755pt }
|
|
#G25 { position:absolute;left:4.667pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G25:before {display:inline-block;content:'';height:10.755pt }
|
|
#G26 { position:absolute;left:10.254pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G26:before {display:inline-block;content:'';height:6.400pt }
|
|
#G27 { position:absolute;left:18.962pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G27:before {display:inline-block;content:'';height:10.755pt }
|
|
#G28 { position:absolute;left:30.962pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G28:before {display:inline-block;content:'';height:10.755pt }
|
|
#G29 { position:absolute;left:36.550pt;top:0;font-family:'cmsy7';font-size:8.400pt;line-height:0;}
|
|
#G29:before {display:inline-block;content:'';height:6.400pt }
|
|
#G30 { position:absolute;left:44.050pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G30:before {display:inline-block;content:'';height:6.400pt }
|
|
#G31 { position:absolute;left:50.092pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G31:before {display:inline-block;content:'';height:10.755pt }
|
|
#G32 { position:absolute;left:54.758pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G32:before {display:inline-block;content:'';height:10.755pt }
|
|
#G33 { position:absolute;left:60.758pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G33:before {display:inline-block;content:'';height:10.755pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy7.ttf') }
|
|
@font-face { font-family: 'cmmi7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi7.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
#G34 { position:absolute;left:0.000pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G34:before {display:inline-block;content:'';height:10.755pt }
|
|
#G35 { position:absolute;left:4.667pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G35:before {display:inline-block;content:'';height:10.755pt }
|
|
#G36 { position:absolute;left:10.254pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G36:before {display:inline-block;content:'';height:6.400pt }
|
|
#G37 { position:absolute;left:18.962pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G37:before {display:inline-block;content:'';height:10.755pt }
|
|
#G38 { position:absolute;left:30.962pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G38:before {display:inline-block;content:'';height:10.755pt }
|
|
#G39 { position:absolute;left:36.550pt;top:0;font-family:'cmsy7';font-size:8.400pt;line-height:0;}
|
|
#G39:before {display:inline-block;content:'';height:6.400pt }
|
|
#G40 { position:absolute;left:44.050pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G40:before {display:inline-block;content:'';height:6.400pt }
|
|
#G41 { position:absolute;left:50.092pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G41:before {display:inline-block;content:'';height:10.755pt }
|
|
#G42 { position:absolute;left:54.758pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G42:before {display:inline-block;content:'';height:10.755pt }
|
|
#G43 { position:absolute;left:60.758pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G43:before {display:inline-block;content:'';height:10.755pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy7.ttf') }
|
|
@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmmi7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi7.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
#G44 { position:absolute;left:0.000pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G44:before {display:inline-block;content:'';height:10.755pt }
|
|
#G45 { position:absolute;left:4.667pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G45:before {display:inline-block;content:'';height:10.755pt }
|
|
#G46 { position:absolute;left:10.254pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G46:before {display:inline-block;content:'';height:6.400pt }
|
|
#G47 { position:absolute;left:18.962pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G47:before {display:inline-block;content:'';height:10.755pt }
|
|
#G48 { position:absolute;left:30.962pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G48:before {display:inline-block;content:'';height:10.755pt }
|
|
#G49 { position:absolute;left:36.550pt;top:0;font-family:'cmsy7';font-size:8.400pt;line-height:0;}
|
|
#G49:before {display:inline-block;content:'';height:6.400pt }
|
|
#G50 { position:absolute;left:44.050pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G50:before {display:inline-block;content:'';height:6.400pt }
|
|
#G51 { position:absolute;left:50.092pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G51:before {display:inline-block;content:'';height:10.755pt }
|
|
#G52 { position:absolute;left:54.758pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G52:before {display:inline-block;content:'';height:10.755pt }
|
|
#G53 { position:absolute;left:60.758pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G53:before {display:inline-block;content:'';height:10.755pt }
|
|
#G54 { position:absolute;left:65.425pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G54:before {display:inline-block;content:'';height:10.755pt }
|
|
#G55 { position:absolute;left:71.013pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G55:before {display:inline-block;content:'';height:6.400pt }
|
|
#G56 { position:absolute;left:79.721pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G56:before {display:inline-block;content:'';height:10.755pt }
|
|
#G57 { position:absolute;left:91.721pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G57:before {display:inline-block;content:'';height:10.755pt }
|
|
#G58 { position:absolute;left:97.308pt;top:0;font-family:'cmsy7';font-size:8.400pt;line-height:0;}
|
|
#G58:before {display:inline-block;content:'';height:6.400pt }
|
|
#G59 { position:absolute;left:104.808pt;top:0;font-family:'cmmi7';font-size:8.400pt;line-height:0;}
|
|
#G59:before {display:inline-block;content:'';height:6.400pt }
|
|
#G60 { position:absolute;left:110.850pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G60:before {display:inline-block;content:'';height:10.755pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmr7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr7.ttf') }
|
|
@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
@font-face { font-family: 'cmtt9'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmtt9.ttf') }
|
|
#G61 { position:absolute;left:0.000pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G61:before {display:inline-block;content:'';height:11.680pt }
|
|
#G62 { position:absolute;left:21.010pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G62:before {display:inline-block;content:'';height:11.680pt }
|
|
#G63 { position:absolute;left:25.676pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G63:before {display:inline-block;content:'';height:11.680pt }
|
|
#G64 { position:absolute;left:35.201pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G64:before {display:inline-block;content:'';height:11.680pt }
|
|
#G65 { position:absolute;left:47.201pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G65:before {display:inline-block;content:'';height:1.680pt }
|
|
#G66 { position:absolute;left:57.201pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G66:before {display:inline-block;content:'';height:11.680pt }
|
|
#G67 { position:absolute;left:65.868pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G67:before {display:inline-block;content:'';height:11.680pt }
|
|
#G68 { position:absolute;left:77.868pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G68:before {display:inline-block;content:'';height:11.680pt }
|
|
#G69 { position:absolute;left:84.726pt;top:0;font-family:'cmr7';font-size:8.400pt;line-height:0;}
|
|
#G69:before {display:inline-block;content:'';height:8.213pt }
|
|
#G70 { position:absolute;left:90.110pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G70:before {display:inline-block;content:'';height:11.680pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmex10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmex10.ttf') }
|
|
@font-face { font-family: 'cmtt9'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmtt9.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
#G71 { position:absolute;left:0.000pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G71:before {display:inline-block;content:'';height:11.940pt }
|
|
#G72 { position:absolute;left:10.000pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G72:before {display:inline-block;content:'';height:11.940pt }
|
|
#G73 { position:absolute;left:31.010pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G73:before {display:inline-block;content:'';height:11.940pt }
|
|
#G74 { position:absolute;left:35.676pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G74:before {display:inline-block;content:'';height:1.680pt }
|
|
#G75 { position:absolute;left:47.677pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G75:before {display:inline-block;content:'';height:11.940pt }
|
|
#G76 { position:absolute;left:52.343pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G76:before {display:inline-block;content:'';height:11.940pt }
|
|
#G77 { position:absolute;left:61.868pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G77:before {display:inline-block;content:'';height:11.940pt }
|
|
#G78 { position:absolute;left:73.868pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G78:before {display:inline-block;content:'';height:11.940pt }
|
|
#G79 { position:absolute;left:84.535pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G79:before {display:inline-block;content:'';height:11.940pt }
|
|
#G80 { position:absolute;left:90.535pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G80:before {display:inline-block;content:'';height:11.940pt }
|
|
#G81 { position:absolute;left:99.201pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G81:before {display:inline-block;content:'';height:11.940pt }
|
|
#G82 { position:absolute;left:111.201pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G82:before {display:inline-block;content:'';height:1.680pt }
|
|
#G83 { position:absolute;left:123.201pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G83:before {display:inline-block;content:'';height:11.940pt }
|
|
#G84 { position:absolute;left:127.868pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G84:before {display:inline-block;content:'';height:11.940pt }
|
|
#G85 { position:absolute;left:137.393pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G85:before {display:inline-block;content:'';height:11.940pt }
|
|
#G86 { position:absolute;left:149.393pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G86:before {display:inline-block;content:'';height:11.940pt }
|
|
#G87 { position:absolute;left:160.060pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G87:before {display:inline-block;content:'';height:11.940pt }
|
|
#G88 { position:absolute;left:166.060pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G88:before {display:inline-block;content:'';height:11.940pt }
|
|
#G89 { position:absolute;left:172.060pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G89:before {display:inline-block;content:'';height:11.940pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmtt9'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmtt9.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
#G90 { position:absolute;left:0.000pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G90:before {display:inline-block;content:'';height:10.200pt }
|
|
#G91 { position:absolute;left:4.667pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G91:before {display:inline-block;content:'';height:10.200pt }
|
|
#G92 { position:absolute;left:25.676pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G92:before {display:inline-block;content:'';height:10.200pt }
|
|
#G93 { position:absolute;left:39.010pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G93:before {display:inline-block;content:'';height:10.200pt }
|
|
#G94 { position:absolute;left:51.010pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G94:before {display:inline-block;content:'';height:10.200pt }
|
|
#G95 { position:absolute;left:57.868pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G95:before {display:inline-block;content:'';height:10.200pt }
|
|
#G96 { position:absolute;left:65.201pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G96:before {display:inline-block;content:'';height:10.200pt }
|
|
#G97 { position:absolute;left:77.201pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G97:before {display:inline-block;content:'';height:10.200pt }
|
|
#G98 { position:absolute;left:98.211pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G98:before {display:inline-block;content:'';height:10.200pt }
|
|
#G99 { position:absolute;left:111.544pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G99:before {display:inline-block;content:'';height:10.200pt }
|
|
#G100 { position:absolute;left:123.544pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G100:before {display:inline-block;content:'';height:10.200pt }
|
|
#G101 { position:absolute;left:130.403pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G101:before {display:inline-block;content:'';height:10.200pt }
|
|
#G102 { position:absolute;left:139.736pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G102:before {display:inline-block;content:'';height:10.200pt }
|
|
#G103 { position:absolute;left:145.736pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G103:before {display:inline-block;content:'';height:10.200pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmex10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmex10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmtt9'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmtt9.ttf') }
|
|
#G104 { position:absolute;left:0.000pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G104:before {display:inline-block;content:'';height:15.000pt }
|
|
#G105 { position:absolute;left:43.690pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G105:before {display:inline-block;content:'';height:15.000pt }
|
|
#G106 { position:absolute;left:53.131pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G106:before {display:inline-block;content:'';height:15.000pt }
|
|
#G107 { position:absolute;left:65.798pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G107:before {display:inline-block;content:'';height:15.000pt }
|
|
#G108 { position:absolute;left:75.798pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G108:before {display:inline-block;content:'';height:15.000pt }
|
|
#G109 { position:absolute;left:96.808pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G109:before {display:inline-block;content:'';height:1.680pt }
|
|
#G110 { position:absolute;left:103.974pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G110:before {display:inline-block;content:'';height:4.154pt }
|
|
#G111 { position:absolute;left:115.974pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G111:before {display:inline-block;content:'';height:15.000pt }
|
|
#G112 { position:absolute;left:120.641pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G112:before {display:inline-block;content:'';height:15.000pt }
|
|
#G113 { position:absolute;left:129.416pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G113:before {display:inline-block;content:'';height:15.000pt }
|
|
#G114 { position:absolute;left:141.416pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G114:before {display:inline-block;content:'';height:15.000pt }
|
|
#G115 { position:absolute;left:152.083pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G115:before {display:inline-block;content:'';height:15.000pt }
|
|
#G116 { position:absolute;left:158.083pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G116:before {display:inline-block;content:'';height:15.000pt }
|
|
#G117 { position:absolute;left:166.749pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G117:before {display:inline-block;content:'';height:15.000pt }
|
|
#G118 { position:absolute;left:178.749pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G118:before {display:inline-block;content:'';height:4.154pt }
|
|
#G119 { position:absolute;left:190.749pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G119:before {display:inline-block;content:'';height:15.000pt }
|
|
#G120 { position:absolute;left:195.416pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G120:before {display:inline-block;content:'';height:15.000pt }
|
|
#G121 { position:absolute;left:204.191pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G121:before {display:inline-block;content:'';height:15.000pt }
|
|
#G122 { position:absolute;left:216.191pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G122:before {display:inline-block;content:'';height:15.000pt }
|
|
#G123 { position:absolute;left:226.857pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G123:before {display:inline-block;content:'';height:15.000pt }
|
|
#G124 { position:absolute;left:232.858pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G124:before {display:inline-block;content:'';height:15.000pt }
|
|
#G125 { position:absolute;left:238.858pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G125:before {display:inline-block;content:'';height:1.680pt }
|
|
#G126 { position:absolute;left:246.024pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G126:before {display:inline-block;content:'';height:15.000pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmr7'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr7.ttf') }
|
|
@font-face { font-family: 'cmex10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmex10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmtt9'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmtt9.ttf') }
|
|
#G127 { position:absolute;left:0.000pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G127:before {display:inline-block;content:'';height:15.000pt }
|
|
#G128 { position:absolute;left:43.690pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G128:before {display:inline-block;content:'';height:15.000pt }
|
|
#G129 { position:absolute;left:53.131pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G129:before {display:inline-block;content:'';height:15.000pt }
|
|
#G130 { position:absolute;left:65.798pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G130:before {display:inline-block;content:'';height:15.000pt }
|
|
#G131 { position:absolute;left:86.808pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G131:before {display:inline-block;content:'';height:1.680pt }
|
|
#G132 { position:absolute;left:93.974pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G132:before {display:inline-block;content:'';height:15.000pt }
|
|
#G133 { position:absolute;left:102.749pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G133:before {display:inline-block;content:'';height:15.000pt }
|
|
#G134 { position:absolute;left:114.749pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G134:before {display:inline-block;content:'';height:3.214pt }
|
|
#G135 { position:absolute;left:126.749pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G135:before {display:inline-block;content:'';height:15.000pt }
|
|
#G136 { position:absolute;left:135.416pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G136:before {display:inline-block;content:'';height:15.000pt }
|
|
#G137 { position:absolute;left:147.416pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G137:before {display:inline-block;content:'';height:15.000pt }
|
|
#G138 { position:absolute;left:153.524pt;top:0;font-family:'cmr7';font-size:8.400pt;line-height:0;}
|
|
#G138:before {display:inline-block;content:'';height:11.533pt }
|
|
#G139 { position:absolute;left:158.907pt;top:0;font-family:'cmex10';font-size:12.000pt;line-height:0;}
|
|
#G139:before {display:inline-block;content:'';height:1.680pt }
|
|
#G140 { position:absolute;left:166.074pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G140:before {display:inline-block;content:'';height:15.000pt }
|
|
</STYLE
|
|
><STYLE
|
|
>@font-face { font-family: 'cmsy10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmsy10.ttf') }
|
|
@font-face { font-family: 'cmr10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmr10.ttf') }
|
|
@font-face { font-family: 'cmmi10'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmmi10.ttf') }
|
|
@font-face { font-family: 'cmtt9'; src: url('https://novaspec.org/cl/fonts/bakoma/ttf/cmtt9.ttf') }
|
|
#G141 { position:absolute;left:0.000pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G141:before {display:inline-block;content:'';height:18.318pt }
|
|
#G142 { position:absolute;left:43.690pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G142:before {display:inline-block;content:'';height:18.318pt }
|
|
#G143 { position:absolute;left:53.131pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G143:before {display:inline-block;content:'';height:18.318pt }
|
|
#G144 { position:absolute;left:67.238pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G144:before {display:inline-block;content:'';height:10.200pt }
|
|
#G145 { position:absolute;left:88.248pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G145:before {display:inline-block;content:'';height:10.200pt }
|
|
#G146 { position:absolute;left:101.581pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G146:before {display:inline-block;content:'';height:10.200pt }
|
|
#G147 { position:absolute;left:113.581pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G147:before {display:inline-block;content:'';height:10.200pt }
|
|
#G148 { position:absolute;left:119.689pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G148:before {display:inline-block;content:'';height:10.200pt }
|
|
#G149 { position:absolute;left:127.022pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G149:before {display:inline-block;content:'';height:10.200pt }
|
|
#G150 { position:absolute;left:139.022pt;top:0;font-family:'cmtt9';font-size:10.800pt;line-height:0;}
|
|
#G150:before {display:inline-block;content:'';height:10.200pt }
|
|
#G151 { position:absolute;left:160.032pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G151:before {display:inline-block;content:'';height:10.200pt }
|
|
#G152 { position:absolute;left:173.366pt;top:0;font-family:'cmsy10';font-size:12.000pt;line-height:0;}
|
|
#G152:before {display:inline-block;content:'';height:10.200pt }
|
|
#G153 { position:absolute;left:185.366pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G153:before {display:inline-block;content:'';height:10.200pt }
|
|
#G154 { position:absolute;left:191.474pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G154:before {display:inline-block;content:'';height:10.200pt }
|
|
#G155 { position:absolute;left:128.689pt;top:0;font-family:'cmr10';font-size:12.000pt;line-height:0;}
|
|
#G155:before {display:inline-block;content:'';height:26.549pt }
|
|
#G156 { position:absolute;left:197.581pt;top:0;font-family:'cmmi10';font-size:12.000pt;line-height:0;}
|
|
#G156:before {display:inline-block;content:'';height:18.318pt }
|
|
</STYLE
|
|
></HEAD
|
|
><BODY
|
|
><DIV
|
|
><DIV CLASS="topnav"
|
|
><DIV CLASS="breadcrumb"
|
|
><SPAN CLASS="breadcrumb-item"
|
|
><A HREF="index.html"
|
|
>Common Lisp Nova Spec</A
|
|
></SPAN
|
|
> <SPAN CLASS="breadcrumb-item"
|
|
>→ <A HREF="12_Numbers.html"
|
|
>12. Numbers</A
|
|
></SPAN
|
|
> <SPAN CLASS="breadcrumb-item"
|
|
>→ <A HREF="12_2_Numbers_Dictionary.html"
|
|
>12.2 Numbers Dictionary</A
|
|
></SPAN
|
|
> <SPAN CLASS="breadcrumb-item"
|
|
>→ <A HREF="f_sinh.html"
|
|
>sinh, cosh, tanh, asinh, acosh, atanh</A
|
|
></SPAN
|
|
></DIV
|
|
><DIV CLASS="apropos"
|
|
><DIV CLASS="apropos-io"
|
|
><A HREF="v_pi.html" CLASS="prev"
|
|
>←</A
|
|
><SPAN ID="apropos-label"
|
|
>Apropos </SPAN
|
|
><INPUT ID="apropos" AUTOFOCUS="AUTOFOCUS" PLACEHOLDER="Type here to search" ONINPUT="aproposInput(this);" ONKEYUP="aproposKeyup(event);" ONCHANGE="aproposChange(this);" ONFOCUS="aproposFocus(this);" ONFOCUSOUT="aproposFocusout(this);"
|
|
><A HREF="f__star.html" CLASS="next"
|
|
>→</A
|
|
></DIV
|
|
><DIV ID="apropos-res"
|
|
></DIV
|
|
></DIV
|
|
></DIV
|
|
><DIV CLASS="matter"
|
|
><DIV CLASS="com"
|
|
><DIV CLASS="begincom"
|
|
><HR
|
|
><TABLE WIDTH="100%" CELLSPACING="0" CELLPADDING="0"
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" WIDTH="100%" CLASS="name"
|
|
><SPAN CLASS="idx" DATA-KIND="idxref" DATA-TERM="sinh, cosh, tanh, asinh, acosh, atanh"
|
|
></SPAN
|
|
><B
|
|
>sinh, cosh, tanh, asinh, acosh, atanh</B
|
|
></TD
|
|
><TD ALIGN="RIGHT" VALIGN="BASELINE" WIDTH="0" NOWRAP="NOWRAP" CLASS="ftype"
|
|
><I
|
|
>Function</I
|
|
></TD
|
|
></TR
|
|
></TABLE
|
|
><HR
|
|
></DIV
|
|
><UL CLASS="subtoc"
|
|
></UL
|
|
><DL
|
|
><DT
|
|
><B
|
|
>Syntax</B
|
|
></DT
|
|
><DD
|
|
><P CLASS="j"
|
|
><B
|
|
>sinh</B
|
|
> <SPAN CLASS="cmssi"
|
|
>number</SPAN
|
|
> <SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
> <SPAN CLASS="cmssi"
|
|
>result</SPAN
|
|
></P
|
|
><P CLASS="j"
|
|
><B
|
|
>cosh</B
|
|
> <SPAN CLASS="cmssi"
|
|
>number</SPAN
|
|
> <SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
> <SPAN CLASS="cmssi"
|
|
>result</SPAN
|
|
></P
|
|
><P CLASS="j"
|
|
><B
|
|
>tanh</B
|
|
> <SPAN CLASS="cmssi"
|
|
>number</SPAN
|
|
> <SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
> <SPAN CLASS="cmssi"
|
|
>result</SPAN
|
|
></P
|
|
><P CLASS="j"
|
|
><B
|
|
>asinh</B
|
|
> <SPAN CLASS="cmssi"
|
|
>number</SPAN
|
|
> <SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
> <SPAN CLASS="cmssi"
|
|
>result</SPAN
|
|
></P
|
|
><P CLASS="j"
|
|
><B
|
|
>acosh</B
|
|
> <SPAN CLASS="cmssi"
|
|
>number</SPAN
|
|
> <SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
> <SPAN CLASS="cmssi"
|
|
>result</SPAN
|
|
></P
|
|
><P CLASS="j"
|
|
><B
|
|
>atanh</B
|
|
> <SPAN CLASS="cmssi"
|
|
>number</SPAN
|
|
> <SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
> <SPAN CLASS="cmssi"
|
|
>result</SPAN
|
|
></P
|
|
></DD
|
|
><DT
|
|
><B
|
|
>Arguments and Values</B
|
|
></DT
|
|
><DD
|
|
><P CLASS="j"
|
|
><VAR CLASS="param"
|
|
>number</VAR
|
|
> — a <A HREF="26_1_Glossary.html#number"
|
|
><EM CLASS="term"
|
|
>number</EM
|
|
></A
|
|
>. </P
|
|
><P CLASS="j"
|
|
><VAR CLASS="param"
|
|
>result</VAR
|
|
> — a <A HREF="26_1_Glossary.html#number"
|
|
><EM CLASS="term"
|
|
>number</EM
|
|
></A
|
|
>.</P
|
|
></DD
|
|
><DT
|
|
><B
|
|
>Description</B
|
|
></DT
|
|
><DD
|
|
><P CLASS="j"
|
|
>These functions compute the hyperbolic sine, cosine, tangent, arc sine, arc cosine, and arc tangent functions, which are mathematically defined for an argument <I CLASS="i"
|
|
><I
|
|
>x</I
|
|
></I
|
|
> as given in Figure 12–16.</P
|
|
><FIGURE CLASS="boxfig"
|
|
><DIV CLASS="figbody"
|
|
><TABLE CELLSPACING="0" CELLPADDING="0" RULES="GROUPS" STYLE="margin: 1ex 0" WIDTH="100%"
|
|
><THEAD
|
|
><TR
|
|
><TH ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
><B
|
|
>Function</B
|
|
></TH
|
|
><TH ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <B
|
|
>Definition</B
|
|
></TH
|
|
></TR
|
|
></THEAD
|
|
><TBODY
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
> <SPAN CLASS="cmr"
|
|
>Hyperbolic</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>sine</SPAN
|
|
></TD
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <SPAN STYLE="display:inline-block;position:relative;width:66.758pt;height:14.955pt;vertical-align:-4.200pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G24"
|
|
>(</SPAN
|
|
><SPAN ID="G25"
|
|
>e</SPAN
|
|
><SPAN ID="G26"
|
|
>x</SPAN
|
|
><SPAN ID="G27"
|
|
>¡</SPAN
|
|
><SPAN ID="G28"
|
|
>e</SPAN
|
|
><SPAN ID="G29"
|
|
>¡</SPAN
|
|
><SPAN ID="G30"
|
|
>x</SPAN
|
|
><SPAN ID="G31"
|
|
>)</SPAN
|
|
><SPAN ID="G32"
|
|
>=</SPAN
|
|
><SPAN ID="G33"
|
|
>2</SPAN
|
|
></SPAN
|
|
></TD
|
|
></TR
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
> <SPAN CLASS="cmr"
|
|
>Hyperbolic</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>cosine</SPAN
|
|
></TD
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <SPAN STYLE="display:inline-block;position:relative;width:66.758pt;height:14.955pt;vertical-align:-4.200pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G34"
|
|
>(</SPAN
|
|
><SPAN ID="G35"
|
|
>e</SPAN
|
|
><SPAN ID="G36"
|
|
>x</SPAN
|
|
><SPAN ID="G37"
|
|
>+</SPAN
|
|
><SPAN ID="G38"
|
|
>e</SPAN
|
|
><SPAN ID="G39"
|
|
>¡</SPAN
|
|
><SPAN ID="G40"
|
|
>x</SPAN
|
|
><SPAN ID="G41"
|
|
>)</SPAN
|
|
><SPAN ID="G42"
|
|
>=</SPAN
|
|
><SPAN ID="G43"
|
|
>2</SPAN
|
|
></SPAN
|
|
></TD
|
|
></TR
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
> <SPAN CLASS="cmr"
|
|
>Hyperbolic</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>tangent</SPAN
|
|
></TD
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <SPAN STYLE="display:inline-block;position:relative;width:115.517pt;height:14.955pt;vertical-align:-4.200pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G44"
|
|
>(</SPAN
|
|
><SPAN ID="G45"
|
|
>e</SPAN
|
|
><SPAN ID="G46"
|
|
>x</SPAN
|
|
><SPAN ID="G47"
|
|
>¡</SPAN
|
|
><SPAN ID="G48"
|
|
>e</SPAN
|
|
><SPAN ID="G49"
|
|
>¡</SPAN
|
|
><SPAN ID="G50"
|
|
>x</SPAN
|
|
><SPAN ID="G51"
|
|
>)</SPAN
|
|
><SPAN ID="G52"
|
|
>=</SPAN
|
|
><SPAN ID="G53"
|
|
>(</SPAN
|
|
><SPAN ID="G54"
|
|
>e</SPAN
|
|
><SPAN ID="G55"
|
|
>x</SPAN
|
|
><SPAN ID="G56"
|
|
>+</SPAN
|
|
><SPAN ID="G57"
|
|
>e</SPAN
|
|
><SPAN ID="G58"
|
|
>¡</SPAN
|
|
><SPAN ID="G59"
|
|
>x</SPAN
|
|
><SPAN ID="G60"
|
|
>)</SPAN
|
|
></SPAN
|
|
></TD
|
|
></TR
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
> <SPAN CLASS="cmr"
|
|
>Hyperbolic</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>arc</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>sine</SPAN
|
|
></TD
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <SPAN STYLE="display:inline-block;position:relative;width:94.776pt;height:15.880pt;vertical-align:-4.200pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G61"
|
|
>log</SPAN
|
|
><SPAN ID="G62"
|
|
>(</SPAN
|
|
><SPAN ID="G63"
|
|
>x</SPAN
|
|
><SPAN ID="G64"
|
|
>+</SPAN
|
|
><SPAN ID="G65"
|
|
>p</SPAN
|
|
><SPAN STYLE="position:absolute;left:57.201pt;top:0.720pt;width:32.908pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G66"
|
|
>1</SPAN
|
|
><SPAN ID="G67"
|
|
>+</SPAN
|
|
><SPAN ID="G68"
|
|
>x</SPAN
|
|
><SPAN ID="G69"
|
|
>2</SPAN
|
|
><SPAN ID="G70"
|
|
>)</SPAN
|
|
></SPAN
|
|
></TD
|
|
></TR
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
> <SPAN CLASS="cmr"
|
|
>Hyperbolic</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>arc</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>cosine</SPAN
|
|
></TD
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <SPAN STYLE="display:inline-block;position:relative;width:176.726pt;height:16.800pt;vertical-align:-4.860pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G71"
|
|
>2</SPAN
|
|
><SPAN ID="G72"
|
|
>log</SPAN
|
|
><SPAN ID="G73"
|
|
>(</SPAN
|
|
><SPAN ID="G74"
|
|
>p</SPAN
|
|
><SPAN STYLE="position:absolute;left:47.677pt;top:0.720pt;width:48.858pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G75"
|
|
>(</SPAN
|
|
><SPAN ID="G76"
|
|
>x</SPAN
|
|
><SPAN ID="G77"
|
|
>+</SPAN
|
|
><SPAN ID="G78"
|
|
>1)</SPAN
|
|
><SPAN ID="G79"
|
|
>=</SPAN
|
|
><SPAN ID="G80"
|
|
>2</SPAN
|
|
><SPAN ID="G81"
|
|
>+</SPAN
|
|
><SPAN ID="G82"
|
|
>p</SPAN
|
|
><SPAN STYLE="position:absolute;left:123.201pt;top:0.720pt;width:48.858pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G83"
|
|
>(</SPAN
|
|
><SPAN ID="G84"
|
|
>x</SPAN
|
|
><SPAN ID="G85"
|
|
>¡</SPAN
|
|
><SPAN ID="G86"
|
|
>1)</SPAN
|
|
><SPAN ID="G87"
|
|
>=</SPAN
|
|
><SPAN ID="G88"
|
|
>2</SPAN
|
|
><SPAN ID="G89"
|
|
>)</SPAN
|
|
></SPAN
|
|
></TD
|
|
></TR
|
|
><TR
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE=";padding-right:3px"
|
|
> <SPAN CLASS="cmr"
|
|
>Hyperbolic</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>arc</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>tangent</SPAN
|
|
></TD
|
|
><TD ALIGN="LEFT" VALIGN="BASELINE" STYLE="padding-left:3px;"
|
|
> <SPAN STYLE="display:inline-block;position:relative;width:151.736pt;height:14.400pt;vertical-align:-4.200pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G90"
|
|
>(</SPAN
|
|
><SPAN ID="G91"
|
|
>log</SPAN
|
|
><SPAN ID="G92"
|
|
>(1</SPAN
|
|
><SPAN ID="G93"
|
|
>+</SPAN
|
|
><SPAN ID="G94"
|
|
>x</SPAN
|
|
><SPAN ID="G95"
|
|
>)</SPAN
|
|
><SPAN ID="G96"
|
|
>¡</SPAN
|
|
><SPAN ID="G97"
|
|
>log</SPAN
|
|
><SPAN ID="G98"
|
|
>(1</SPAN
|
|
><SPAN ID="G99"
|
|
>¡</SPAN
|
|
><SPAN ID="G100"
|
|
>x</SPAN
|
|
><SPAN ID="G101"
|
|
>))</SPAN
|
|
><SPAN ID="G102"
|
|
>=</SPAN
|
|
><SPAN ID="G103"
|
|
>2</SPAN
|
|
></SPAN
|
|
></TD
|
|
></TR
|
|
></TBODY
|
|
></TABLE
|
|
></DIV
|
|
><FIGCAPTION CLASS="caption"
|
|
><B
|
|
>Figure 12–16. Mathematical definitions for hyperbolic functions</B
|
|
></FIGCAPTION
|
|
></FIGURE
|
|
><P CLASS="j"
|
|
>The following definition for the inverse hyperbolic cosine determines the range and branch cuts:</P
|
|
><CENTER CLASS="displaymath"
|
|
><SPAN STYLE="display:inline-block;position:relative;width:249.358pt;height:24.000pt;vertical-align:0.000pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G104"
|
|
>arccosh</SPAN
|
|
><SPAN ID="G105"
|
|
>z</SPAN
|
|
><SPAN ID="G106"
|
|
>=</SPAN
|
|
><SPAN ID="G107"
|
|
>2</SPAN
|
|
><SPAN ID="G108"
|
|
>log</SPAN
|
|
><SPAN ID="G109"
|
|
>³</SPAN
|
|
><SPAN ID="G110"
|
|
>p</SPAN
|
|
><SPAN STYLE="position:absolute;left:115.974pt;top:3.194pt;width:48.108pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G111"
|
|
>(</SPAN
|
|
><SPAN ID="G112"
|
|
>z</SPAN
|
|
><SPAN ID="G113"
|
|
>+</SPAN
|
|
><SPAN ID="G114"
|
|
>1)</SPAN
|
|
><SPAN ID="G115"
|
|
>=</SPAN
|
|
><SPAN ID="G116"
|
|
>2</SPAN
|
|
><SPAN ID="G117"
|
|
>+</SPAN
|
|
><SPAN ID="G118"
|
|
>p</SPAN
|
|
><SPAN STYLE="position:absolute;left:190.749pt;top:3.194pt;width:48.108pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G119"
|
|
>(</SPAN
|
|
><SPAN ID="G120"
|
|
>z</SPAN
|
|
><SPAN ID="G121"
|
|
>¡</SPAN
|
|
><SPAN ID="G122"
|
|
>1)</SPAN
|
|
><SPAN ID="G123"
|
|
>=</SPAN
|
|
><SPAN ID="G124"
|
|
>2</SPAN
|
|
><SPAN ID="G125"
|
|
>´</SPAN
|
|
><SPAN ID="G126"
|
|
>:</SPAN
|
|
></SPAN
|
|
></CENTER
|
|
><P CLASS="j"
|
|
>The branch cut for the inverse hyperbolic cosine function lies along the real axis to the left of 1 (inclusive), extending indefinitely along the negative real axis, continuous with quadrant II and (between 0 and 1) with quadrant I. The range is that half-strip of the complex plane containing numbers whose real part is non-negative and whose imaginary part is between −π (exclusive) and π (inclusive). A number with real part zero is in the range if its imaginary part is between zero (inclusive) and π (inclusive). </P
|
|
><P CLASS="j"
|
|
>The following definition for the inverse hyperbolic sine determines the range and branch cuts:</P
|
|
><CENTER CLASS="displaymath"
|
|
><SPAN STYLE="display:inline-block;position:relative;width:169.407pt;height:24.000pt;vertical-align:0.000pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G127"
|
|
>arcsinh</SPAN
|
|
><SPAN ID="G128"
|
|
>z</SPAN
|
|
><SPAN ID="G129"
|
|
>=</SPAN
|
|
><SPAN ID="G130"
|
|
>log</SPAN
|
|
><SPAN ID="G131"
|
|
>³</SPAN
|
|
><SPAN ID="G132"
|
|
>z</SPAN
|
|
><SPAN ID="G133"
|
|
>+</SPAN
|
|
><SPAN ID="G134"
|
|
>p</SPAN
|
|
><SPAN STYLE="position:absolute;left:126.749pt;top:2.254pt;width:32.158pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G135"
|
|
>1</SPAN
|
|
><SPAN ID="G136"
|
|
>+</SPAN
|
|
><SPAN ID="G137"
|
|
>z</SPAN
|
|
><SPAN ID="G138"
|
|
>2</SPAN
|
|
><SPAN ID="G139"
|
|
>´</SPAN
|
|
><SPAN ID="G140"
|
|
>:</SPAN
|
|
></SPAN
|
|
></CENTER
|
|
><P CLASS="j"
|
|
>The branch cut for the inverse hyperbolic sine function is in two pieces: one along the positive imaginary axis above <I
|
|
>i</I
|
|
> (inclusive), continuous with quadrant I, and one along the negative imaginary axis below −<I
|
|
>i</I
|
|
> (inclusive), continuous with quadrant III. The range is that strip of the complex plane containing numbers whose imaginary part is between −π<I
|
|
>/</I
|
|
>2 and π<I
|
|
>/</I
|
|
>2. A number with imaginary part equal to −π<I
|
|
>/</I
|
|
>2 is in the range if and only if its real part is non-positive; a number with imaginary part equal to π<I
|
|
>/</I
|
|
>2 is in the range if and only if its imaginary part is non-negative. </P
|
|
><P CLASS="j"
|
|
>The following definition for the inverse hyperbolic tangent determines the range and branch cuts:</P
|
|
><CENTER CLASS="displaymath"
|
|
><SPAN STYLE="display:inline-block;position:relative;width:200.914pt;height:27.749pt;vertical-align:0.000pt;xborder:1px solid #ccc"
|
|
><SPAN ID="G141"
|
|
>arctanh</SPAN
|
|
><SPAN ID="G142"
|
|
>z</SPAN
|
|
><SPAN ID="G143"
|
|
>=</SPAN
|
|
><SPAN ID="G144"
|
|
>log</SPAN
|
|
><SPAN ID="G145"
|
|
>(1</SPAN
|
|
><SPAN ID="G146"
|
|
>+</SPAN
|
|
><SPAN ID="G147"
|
|
>z</SPAN
|
|
><SPAN ID="G148"
|
|
>)</SPAN
|
|
><SPAN ID="G149"
|
|
>¡</SPAN
|
|
><SPAN ID="G150"
|
|
>log</SPAN
|
|
><SPAN ID="G151"
|
|
>(1</SPAN
|
|
><SPAN ID="G152"
|
|
>¡</SPAN
|
|
><SPAN ID="G153"
|
|
>z</SPAN
|
|
><SPAN ID="G154"
|
|
>)</SPAN
|
|
><SPAN STYLE="position:absolute;left:67.238pt;top:14.598pt;width:128.903pt;border-bottom:0.960pt solid black;"
|
|
></SPAN
|
|
><SPAN ID="G155"
|
|
>2</SPAN
|
|
><SPAN ID="G156"
|
|
>:</SPAN
|
|
></SPAN
|
|
></CENTER
|
|
><P CLASS="j"
|
|
>Note that:</P
|
|
><DIV CLASS="displaymath"
|
|
><I
|
|
>i</I
|
|
> <SPAN CLASS="cmtt"
|
|
>arctan</SPAN
|
|
> <I
|
|
>z</I
|
|
><SPAN CLASS="cmr"
|
|
>=</SPAN
|
|
><SPAN CLASS="cmtt"
|
|
>arctanh</SPAN
|
|
> <I
|
|
>iz.</I
|
|
></DIV
|
|
><P CLASS="j"
|
|
>The branch cut for the inverse hyperbolic tangent function is in two pieces: one along the negative real axis to the left of −1 (inclusive), continuous with quadrant III, and one along the positive real axis to the right of 1 (inclusive), continuous with quadrant I. The points −1 and 1 are excluded from the domain. The range is that strip of the complex plane containing numbers whose imaginary part is between −π<I
|
|
>/</I
|
|
>2 and π<I
|
|
>/</I
|
|
>2. A number with imaginary part equal to −π<I
|
|
>/</I
|
|
>2 is in the range if and only if its real part is strictly negative; a number with imaginary part equal to π<I
|
|
>/</I
|
|
>2 is in the range if and only if its imaginary part is strictly positive. Thus the range of the inverse hyperbolic tangent function is identical to that of the inverse hyperbolic sine function with the points −π<I
|
|
>i/</I
|
|
>2 and π<I
|
|
>i/</I
|
|
>2 excluded.</P
|
|
></DD
|
|
><DT
|
|
><B
|
|
>Examples</B
|
|
></DT
|
|
><DD
|
|
><PRE CLASS="screen"
|
|
>(sinh 0) <SPAN CLASS="cmsy"
|
|
><SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
></SPAN
|
|
> 0.0
|
|
(cosh (complex 0 -1)) <SPAN CLASS="cmsy"
|
|
><SPAN CLASS="arrow"
|
|
>→</SPAN
|
|
></SPAN
|
|
> #C(0.540302 -0.0)</PRE
|
|
></DD
|
|
><DT
|
|
><B
|
|
>Exceptional Situations</B
|
|
></DT
|
|
><DD
|
|
><P CLASS="j"
|
|
>Should signal an error of <A HREF="26_1_Glossary.html#type"
|
|
><EM CLASS="term"
|
|
>type</EM
|
|
></A
|
|
> <A HREF="t_type-error.html" CLASS="typeref"
|
|
><B
|
|
>type-error</B
|
|
></A
|
|
> if <VAR CLASS="param"
|
|
>number</VAR
|
|
> is not a <A HREF="26_1_Glossary.html#number"
|
|
><EM CLASS="term"
|
|
>number</EM
|
|
></A
|
|
>. Might signal <A HREF="t_arithmetic-error.html" CLASS="typeref"
|
|
><B
|
|
>arithmetic-error</B
|
|
></A
|
|
>.</P
|
|
></DD
|
|
><DT
|
|
><B
|
|
>See Also</B
|
|
></DT
|
|
><DD
|
|
><P CLASS="j"
|
|
><A HREF="f_log.html" CLASS="funref"
|
|
><B
|
|
>log</B
|
|
></A
|
|
>, <A HREF="f_sqrt.html" CLASS="funref"
|
|
><B
|
|
>sqrt</B
|
|
></A
|
|
>, <A HREF="12_1_Number_Concepts.html#sec_12_1_3_3" CLASS="secref"
|
|
><SPAN CLASS="cmr"
|
|
>Section</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>12.1.3.3</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>(Rule</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>of</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>Float</SPAN
|
|
> <SPAN CLASS="cmr"
|
|
>Substitutability)</SPAN
|
|
></A
|
|
></P
|
|
></DD
|
|
><DT
|
|
><B
|
|
>Notes</B
|
|
></DT
|
|
><DD
|
|
><P CLASS="j"
|
|
>The result of <A HREF="f_sinh.html" CLASS="funref"
|
|
><B
|
|
>acosh</B
|
|
></A
|
|
> may be a <A HREF="26_1_Glossary.html#complex"
|
|
><EM CLASS="term"
|
|
>complex</EM
|
|
></A
|
|
> even if <VAR CLASS="param"
|
|
>number</VAR
|
|
> is not a <A HREF="26_1_Glossary.html#complex"
|
|
><EM CLASS="term"
|
|
>complex</EM
|
|
></A
|
|
>; this occurs when <VAR CLASS="param"
|
|
>number</VAR
|
|
> is less than one. Also, the result of <A HREF="f_sinh.html" CLASS="funref"
|
|
><B
|
|
>atanh</B
|
|
></A
|
|
> may be a <A HREF="26_1_Glossary.html#complex"
|
|
><EM CLASS="term"
|
|
>complex</EM
|
|
></A
|
|
> even if <VAR CLASS="param"
|
|
>number</VAR
|
|
> is not a <A HREF="26_1_Glossary.html#complex"
|
|
><EM CLASS="term"
|
|
>complex</EM
|
|
></A
|
|
>; this occurs when the absolute value of <VAR CLASS="param"
|
|
>number</VAR
|
|
> is greater than one. </P
|
|
><P CLASS="j"
|
|
>The branch cut formulae are mathematically correct, assuming completely accurate computation. Implementors should consult a good text on numerical analysis. The formulae given above are not necessarily the simplest ones for real-valued computations; they are chosen to define the branch cuts in desirable ways for the complex case.</P
|
|
></DD
|
|
></DL
|
|
></DIV
|
|
></DIV
|
|
><DIV CLASS="footer"
|
|
><DIV CLASS="btmnav"
|
|
><A HREF="v_pi.html" CLASS="prev"
|
|
>←</A
|
|
><A HREF="f__star.html" CLASS="next"
|
|
>→</A
|
|
></DIV
|
|
><DIV CLASS="trail"
|
|
>Conversion to HTML copyright 2023 by Gilbert Baumann</DIV
|
|
></DIV
|
|
></DIV
|
|
><SCRIPT
|
|
>domReady();</SCRIPT
|
|
></BODY
|
|
></HTML
|
|
> |