[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572380-105":53,"doc-detail-572380-en":126},{"code":4,"msg":5,"data":6},0,"success",[7,14,19,24,29,34,39,44,49],{"id":8,"doc_module":9,"doc_module_name":10,"category_name":11,"show_sort_weight":12,"slug":13},11,1,"Template","Presentations",90,"presentations",{"id":15,"doc_module":9,"doc_module_name":10,"category_name":16,"show_sort_weight":17,"slug":18},12,"Resumes",80,"resumes",{"id":20,"doc_module":9,"doc_module_name":10,"category_name":21,"show_sort_weight":22,"slug":23},14,"Invoices",70,"invoices",{"id":25,"doc_module":9,"doc_module_name":10,"category_name":26,"show_sort_weight":27,"slug":28},15,"Posters",60,"posters",{"id":30,"doc_module":9,"doc_module_name":10,"category_name":31,"show_sort_weight":32,"slug":33},16,"Social Media",50,"social-media",{"id":35,"doc_module":9,"doc_module_name":10,"category_name":36,"show_sort_weight":37,"slug":38},17,"Forms",40,"forms",{"id":40,"doc_module":9,"doc_module_name":10,"category_name":41,"show_sort_weight":42,"slug":43},18,"Letters",30,"letters",{"id":45,"doc_module":9,"doc_module_name":10,"category_name":46,"show_sort_weight":47,"slug":48},21,"Paper Templates",5,"papers-templates",{"id":50,"doc_module":9,"doc_module_name":10,"category_name":51,"show_sort_weight":4,"slug":52},158,"General","general-158",{"code":4,"msg":54,"data":55},"ok",{"site_id":56,"language":57,"slug":58,"title":59,"keywords":60,"description":61,"schema_data":62,"social_meta":119,"head_meta":121,"extra_data":123,"updated_unix":125},105,"en","trigonometry-full-sheet-right-angle-triangle-trigonometric-functions","TRIGONOMETRY-Full Sheet - Right Angle Triangle - Trigonometric Functions","","TRIGONOMETRY-Full Sheet covers right angle triangles and introduces Pythagorean triplets, including common examples like (3,4,5) and (5,12,13). It summarizes key trigonometric functions with a table for standard angles, including sin, cos, tan, cosec, sec, and cot. The sheet explains angle relationships and complementary rules (A+B=90°), degree–radian conversions, arc length in terms of radius and radian measure, and multiple trigonometric identities for sums, differences, and double-angle style forms.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":46,"@type":70,"position":76},"https://docshare.wps.com/template/paper-templates/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/trigonometry-full-sheet-right-angle-triangle-trigonometric-functions/572380/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/trigonometry-full-sheet-right-angle-triangle-trigonometric-functions/572380.png","ImageObject",442,249,{"name":88,"@type":89},"supergirl","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":9},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"What is a Pythagorean triplet and how is it defined?","Question",{"text":108,"@type":109},"A Pythagorean triplet is a set of positive integers a, b and c that satisfies a rule stated on the sheet and is shown in the form presented in the document. The sheet also lists several examples such as (3,4,5) and (5,12,13).","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What does the angles rule A + B = 90° imply for sin, cos, tan, cot?",{"text":113,"@type":109},"When A + B = 90°, the sheet gives complementary relationships such as Sin A = Cos B and Tan A = Cot B, with corresponding reciprocal links between sec/cosec and the complementary angle functions.",{"name":115,"@type":106,"acceptedAnswer":116},"How are degrees and radians related, and how is arc length computed?",{"text":117,"@type":109},"The sheet states that ∏ radian = 180 degree and provides conversions for minute and second angles. It also states that length of arc equals radius of circle multiplied by the angle in radian, and that arc length is directly proportional to the radius.","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},572380,1792053098,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":45,"category_name":46,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":9,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":135,"language":136,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":137,"faqs":138,"seo_title":139,"seo_description":61,"update_tm":140,"read_time":141},962088121634,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","TRIGONOMETRY-Full Sheet  \nRight Angle Triangle  \n􀁹 One angle is 90  \nPythagorean Triplet: -  \n􀁹 A “ Pythagorean Triplet” is a set of positive integers a, band c that fits the rule   \n􀁹 Triplet is in the form of   \n􀁹 Some example of Basic Pythagorean triplet –(3, 4, 5) (5, 12, 13) (7, 24, 25) (8, 15,17)(9, 40, 41) (11, 60, 61) (12, 35, 37) (13, 84, 85)(16, 63, 65) (20, 21, 29) (28, 45, 53) (33, 56, 65)(36, 77, 85) (39, 80, 89) (48, 55, 73) (65, 72, 97)  \n(20, 99, 101) Power Mind institute  \nTrigonometric functions  \nFormula:-  \nPower Mind institute  \nFormula-  \nFormula  \nPower Mind institute  \nTrigonometry Table  \n\n| Angles Ratios | 0 | 30 | 45 | 60 | 90 |\n| --- | --- | --- | --- | --- | --- |\n| Sin 􀁔 | 0 | 􀫚􀫛 |  􀫚   􀫛 | 􀫜\u003Cbr>\u003Cbr>􀫛 | 1 |\n| Cos 􀁔 | 1 | 􀫜\u003Cbr>\u003Cbr>􀫛 |  􀫚   􀫛 | 􀫚􀫛 | 0 |\n| Tan 􀁔 | 0 |  􀫚 􀫜\u003Cbr>| 1 |  􀫜 | ∞ |\n| Cosec 􀁔 | ∞ | 2 |  􀫛 |  􀫛 􀫜\u003Cbr>| 1 |\n| Sec 􀁔 | 1 |  􀫛 􀫜\u003Cbr>|  􀫛 | 2 | ∞ |\n| Cot 􀁔 | ∞ |  􀫜 | 1 | 􀫚\u003Cbr>􀫜\u003Cbr>| 0 |\n\nPower Mind institute  \nImportant Concept  \nAngles rule  \nPower Mind institute  \nConcept  \n􀁹 If A + B = 90 􀁱  \nThen  \nSin A = Cos B & SinA.SecB=1  \nTan A = Cot B & TanA.TanB =1 & CotA.CotB=1 Sec A = Cosec B & CosA.CosecB=1  \nConcept of degree  \n􀁹 ∏ radian = 180 degree  \n􀁹 1 degree = 60 minute angle  \n􀁹 1 minute angle = 60 second angle  \n􀁹 1 radian = 57 degree 16 minute 22 second.  \n􀁹 Length of arc = radius of circle * angle in radian  \n􀁹 Length of arc is directly proportional to radius of circle.  \nPower Mind institute  \nConcept based on sin and cos  \nIf   \nThen   \nIf   \nIf   \nThen   \nConcept based on sec, tan cosec , cot  \nPower Mind institute  \nConcept  \n􀁹 If   \n􀁹 Then   \n􀁹 If   \n􀁹 Then   \nFormula of Trigonometry  \n􀁹 Sin(A+B) = sinA cosB + cosA sinB  \n􀁹 Sin(A-B) = sinA cosB – cosA sinB  \n􀁹 Cos (A+B) = CosA cosB – sinA sinB  \n􀁹 Cos(A-B) = cosA cosB + sinAsinB  \n􀁹 2sinAcosB = sin(A+B) + sin (A-B)  \n􀁹 2cosAsinB = sin(A+B)– sin(A-B)  \n􀁹 2cosAcosB = cos(A+B) + cos(A-B)  \n􀁹 2sinAsinB = cos(A-B)–cos(A+B)  \n\n| |\n| --- |\n| |\n\nPower Mind institute  \nFormula  \n􀁹 sinC + sinD = 2sin ~~ ~~􀡯~~ ~~~~ ~~􀡰 cos 􀡯~~ ~~~~ ~~􀡰􀁹 sinC – sinD = 2cos ~~ ~~􀡯~~ ~~~~ ~~􀡰 sin 􀡯~~ ~~~~ ~~􀡰􀁹 cosC + cosD = 2cos 􀡯~~ ~~~~ ~~􀡰~~ ~~ cos 􀡯~~ ~~~~ ~~􀡰􀁹 cosC – cosD = 2sin ~~ ~~􀡯~~ ~~~~ ~~􀡰 sin 􀡰~~ ~~~~ ~~􀡯  \n􀁹  \nImportant Formula  \n􀁹 Tan (A+B) = 􀫚􀜜􀜜􀡭􀜉􀜖+􀡭􀜜􀜉􀜜􀜖􀜉􀜖􀡮􀡮  \n􀁹 Tan (A-B) = ~~ ~~􀫚􀜜􀜜􀡭􀜉􀜖−􀡭􀜜􀜉􀜜􀜖􀜉􀜖􀡮􀡮  \n􀁹 Cot (A+B) = 􀜋􀜗􀜋􀜜􀜗􀡭~~ ~~􀜋􀜜~~ ~~􀡮􀜜~~ ~~􀡮􀜋􀜗􀡭􀫚  \n􀁹 Cot (A-B) = 􀜋􀜗􀜋􀜜􀜗􀡭~~ ~~􀜋􀜜~~ ~~􀡮􀜜~~ ~~􀡮􀜋􀜗􀡭􀫚  \nPower Mind institute  \nSome Other value of trigonometry ratio  \n􀁱 􀁱 ~~ ~~3 +1 sin75 = cos15 = ~~ ~~  \n2~~ ~~2  \n􀁱 􀁱 ~~ ~~3 −1 sin15 = cos75 = ~~   ~~  \n2~~ ~~2  \n3 +1 ~~ ~~  \ncot15􀁱 = tan75􀁱 = ~~ ~~ = 2+ 3  \n3 −1  \ncot75􀁱 = tan15􀁱 = 33~~ ~~~~ ~~11 = 2 − 3  \nImportant Concept  \n􀁹 If  \n􀁹 If  \n􀁹 If  \n􀁹 If  \n􀜜􀜉􀜖 ( 􀡭 + 􀡮 + 􀡯) =  \n 􀜜􀜉􀜖 􀡭 + 􀜜􀜉􀜖 􀡮 + 􀜜􀜉􀜖 􀡯 − 􀜜􀜉􀜖 􀡭 􀜜􀜉􀜖 􀡮 􀜜􀜉􀜖 􀡯 􀫚 − 􀜜􀜉􀜖 􀡭 􀜜􀜉􀜖 􀡮 − 􀜜􀜉􀜖 􀡮 􀜜􀜉􀜖 􀡯 − 􀜜􀜉􀜖 􀡯 􀜜􀜉􀜖 􀡭  \n􀡭 + 􀡮 = 􀫝􀫞°􀢕􀢘􀫛􀫛􀫞°  \n􀢚􀢎􀢋􀢔 (􀫚 + 􀜜􀜉􀜖 􀡭)(􀫚 + 􀜜􀜉􀜖 􀡮) = 􀫛  \n􀡭 + 􀡮 = 􀫝􀫞°􀢕􀢘􀫛􀫛􀫞°  \n􀢚􀢎􀢋􀢔 (􀫚 − 􀜋􀜗􀜜 􀡭)(􀫚 − 􀜋􀜗􀜜 􀡮) = 􀫛  \n􀡭 + 􀡮 + 􀡯 = 􀫢􀫙°  \n􀢀􀢎􀢋􀢔 􀜜􀜉􀜖 􀡭 􀜜􀜉􀜖 􀡮 + 􀜜􀜉􀜖 􀡮 􀜜􀜉􀜖 􀡯 + 􀜜􀜉􀜖 􀡯 􀜜􀜉􀜖 􀡭 = 􀫚& 􀜋􀜗􀜜 􀡭 􀜋􀜗􀜜 􀡮 􀜋􀜗􀜜 􀡯 = 􀜋􀜗􀜜 􀡭 + 􀜋􀜗􀜜 􀡮 + 􀜋􀜗􀜜 􀡯  \n􀡭 + 􀡮 + 􀡯 = 􀫚􀫡􀫙°  \n􀢚􀢎􀢋􀢔 􀜜􀜉􀜖 􀡭 + 􀜜􀜉􀜖 􀡮 + 􀜜􀜉􀜖 􀡯 = 􀜜􀜉􀜖 􀡭 􀜜􀜉􀜖 􀡮 􀜜􀜉􀜖 􀡯& 􀜋􀜗􀜜 􀡭 􀜋􀜗􀜜 􀡮 + 􀜋􀜗􀜜 􀡮 􀜋􀜗􀜜 􀡯 + 􀜋􀜗􀜜 􀡯 􀜋􀜗􀜜 􀡭 = 􀫚  \nPower Mind institute","cbCaisEjiZRE9OHI","https://ap.wps.com/l/cbCaisEjiZRE9OHI","pdf",7750751,57,"English","# Right Angle Triangle\n## Pythagorean Triplet\n# Trigonometric functions\n## Trigonometry Table\n# Important Concepts\n## Angles rule (A+B=90°)\n## Degree and radian concepts\n# Formula of Trigonometry\n## Sum and difference identities\n## Multiple-angle style identities","[{\"question\":\"What is a Pythagorean triplet and how is it defined?\",\"answer\":\"A Pythagorean triplet is a set of positive integers a, b and c that satisfies a rule stated on the sheet and is shown in the form presented in the document. The sheet also lists several examples such as (3,4,5) and (5,12,13).\"},{\"question\":\"What does the angles rule A + B = 90° imply for sin, cos, tan, cot?\",\"answer\":\"When A + B = 90°, the sheet gives complementary relationships such as Sin A = Cos B and Tan A = Cot B, with corresponding reciprocal links between sec/cosec and the complementary angle functions.\"},{\"question\":\"How are degrees and radians related, and how is arc length computed?\",\"answer\":\"The sheet states that ∏ radian = 180 degree and provides conversions for minute and second angles. It also states that length of arc equals radius of circle multiplied by the angle in radian, and that arc length is directly proportional to the radius.\"}]","TRIGONOMETRY-Full Sheet - Right Angle Triangle - Trigonometric Functions | PDF",1791927083,20]