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File:Gudermannian function.png

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Clarify that the shaded areas are half the magnitude of the named variables (if we define area 1 to mean the area of a unit square)
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The Gudermannian function relates the circular and hyperbolic functions.
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The Gudermannian function is used in the construction of the
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933: 169:. If twice the area of the blue hyperbolic sector is 83:(1,652 Γ— 1,274 pixels, file size: 246 KB, MIME type: 175:, then twice the area of the red circular sector is 137: 117:
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851:Use an area representation of s for consistency. 385:https://creativecommons.org/licenses/by-sa/4.0 98: 391:Creative Commons Attribution-Share Alike 4.0 315: 8: 513:https://commons.wikimedia.org/User:Jacobolus 263:https://www.desmos.com/calculator/yvendpvrig 351:– to copy, distribute and transmit the work 951: 713: 413: 916:The following other wikis use this file: 338:Attribution-Share Alike 4.0 International 961: 953: 893: 687: 671: 653: 637: 619: 603: 583: 567: 547: 531: 464: 448: 431: 428: 409: 402: 891:The following 3 pages use this file: 7: 881:Uploaded own work with UploadWizard 702: 326: 321: 944: 422: 416: 312: 308: 147: 130: 76: 421: 246:The purple point has coordinates 407: 362:Under the following conditions: 333:This file is licensed under the 325: 320: 314: 234:. The red point has coordinates 97: 31: 21: 901:Integral of the secant function 404: 222:The blue point has coordinates 148: 14: 403: 26: 1: 906:Talk:Stereographic projection 690:original creation by uploader 36: 429:Items portrayed in this file 261:Image created using Desmos, 983: 930:Usage on www.wikidata.org 920:Usage on ko.wikipedia.org 376:same or compatible license 167:w:stereographic projection 761:use phi instead of varphi 703: 283: 143:Gudermannian function.png 16: 406: 342: 104:This is a file from the 880: 850: 820: 791:minor stylistic changes 790: 760: 289: 279: 272: 269: 155:w:Gudermannian function 140: 108:. Information from its 157:relates the area of a 111:description page there 46:Size of this preview: 955:Horizontal resolution 896:Gudermannian function 257:w:Mercator projection 70:1,652 Γ— 1,274 pixels 963:Vertical resolution 859:19:02, 28 June 2022 829:20:53, 28 June 2022 799:21:36, 28 June 2022 769:21:41, 28 June 2022 739:16:00, 29 June 2022 357:– to adapt the work 163:w:hyperbolic sector 52:Other resolutions: 491:Wikimedia username 478:author name string 66:1,280 Γ— 987 pixels 970: 969: 912:Global file usage 884: 570:copyright license 415: 299: 298: 161:to the area of a 159:w:circular sector 126: 125: 106:Wikimedia Commons 32:Global file usage 974: 952: 871: 841: 811: 781: 751: 534:copyright status 515: 510: 500: 495: 485: 482: 398: 395: 392: 389: 386: 378:as the original. 335:Creative Commons 329: 328: 324: 323: 318: 317: 285: 275: 253: 245: 233: 221: 216: 215: 212: 209: 201: 200: 197: 194: 184: 174: 152: 144: 138: 122: 101: 100: 94: 88: 86: 73: 62:996 Γ— 768 pixels 58:623 Γ— 480 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927: 926: 914: 913: 909: 908: 903: 898: 889: 888: 883: 882: 879: 875: 872: 868:1,624 Γ— 1,278 866: 861: 856: 853: 852: 849: 845: 842: 838:1,600 Γ— 1,224 836: 831: 826: 823: 822: 819: 815: 812: 808:1,632 Γ— 1,282 806: 801: 796: 793: 792: 789: 785: 782: 778:1,672 Γ— 1,304 776: 771: 766: 763: 762: 759: 755: 752: 748:1,652 Γ— 1,274 746: 741: 736: 732: 731: 728: 725: 722: 719: 716: 709: 708: 693: 688: 686: 685: 684: 683: 682: 681: 677: 674:source of file 672: 670: 669: 668: 667: 666: 657: 654: 652: 651: 650: 649: 648: 647: 643: 638: 636: 635: 634: 633: 632: 623: 620: 618: 617: 616: 615: 614: 613: 609: 604: 602: 601: 600: 599: 598: 589: 584: 582: 581: 580: 579: 578: 577: 573: 568: 566: 565: 564: 563: 562: 553: 548: 546: 545: 544: 543: 542: 541: 537: 532: 530: 529: 528: 527: 526: 504: 503: 489: 488: 476: 475: 474: 473: 472: 468: 465: 463: 462: 461: 460: 459: 458: 454: 449: 447: 446: 445: 444: 443: 437: 432: 430: 427: 426: 425: 424: 423: 412: 411: 408: 405: 382: 381: 380: 379: 369: 360: 359: 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190:= tan 236:(cos 180:= gd 727:User 397:true 394:true 270:Date 248:(0, 153:The 17:File 506:URL 509:: 494:: 481:: 259:. 252:). 244:). 68:| 64:| 60:| 56:| 50:. 250:s 242:Ο† 238:Ο† 232:) 230:ψ 226:ψ 220:. 218:ψ 214:2 211:/ 208:1 203:Ο† 199:2 196:/ 193:1 188:s 182:ψ 178:Ο† 172:ψ 121:. 87:) 72:.

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File:Gudermannian function.png
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311 Γ— 240 pixels
623 Γ— 480 pixels
996 Γ— 768 pixels
1,280 Γ— 987 pixels
1,652 Γ— 1,274 pixels
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https://www.desmos.com/calculator/yvendpvrig
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