[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-571377-105":53,"doc-detail-571377-en":127},{"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":120,"head_meta":122,"extra_data":124,"updated_unix":126},105,"en","trigonometric-identities-cheat-sheet","Trigonometric Identities - Cheat Sheet","","This trigonometric identities cheat sheet serves as a concise reference guide for essential mathematical formulas used in trigonometry. It provides a comprehensive compilation of key identities including quotient, reciprocal, Pythagorean, and co-function identities. Furthermore, the document details advanced formulas such as double-angle, half-angle, angle sum and difference, product-to-sum, and negative or supplement angle identities. Designed for students and professionals, this resource facilitates quick look-ups for complex trigonometric calculations and proofs, ensuring accuracy and efficiency in mathematical problem-solving tasks. The structured presentation makes it an ideal study aid or desk reference for anyone working with calculus or higher-level mathematics.",{"@graph":63,"@context":119},[64,80,102],{"@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":51,"@type":70,"position":76},"https://docshare.wps.com/template/general/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/trigonometric-identities-cheat-sheet/571377/",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/trigonometric-identities-cheat-sheet/571377.png","ImageObject",442,249,{"name":88,"@type":89},"I feel Different","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-27","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",9,{"@type":103,"mainEntity":104},"FAQPage",[105,111,115],{"name":106,"@type":107,"acceptedAnswer":108},"What are the three Pythagorean identities listed?","Question",{"text":109,"@type":110},"The listed Pythagorean identities are sin^2θ + cos^2θ = 1, 1 + tan^2θ = sec^2θ, and 1 + cot^2θ = csc^2θ.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How is the double angle identity for sine expressed?",{"text":114,"@type":110},"The double angle identity for sine is expressed as sin(2θ) = 2 sin(θ) cos(θ).",{"name":116,"@type":107,"acceptedAnswer":117},"What do negative angle identities tell us about cosine?",{"text":118,"@type":110},"Negative angle identities show that cos(-θ) = cos(θ), indicating that the cosine function is an even function.","https://schema.org",{"og:url":78,"og:type":121,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":123,"canonical":78},"index,follow",{"doc_id":125,"site_id":56},571377,1792014483,{"code":4,"msg":5,"data":128},{"doc_id":125,"user_id":129,"nickname":88,"user_avatar":130,"doc_module":9,"category_id":50,"category_name":51,"doc_title":59,"doc_description":61,"doc_content":131,"file_id":132,"file_url":133,"file_type":134,"file_size":135,"view_count":101,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":73,"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":9},962093541761,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Trigonometric Identities Cheat Sheet  \nQuotient Identities  \n• tan  =• cot  =  \nReciprocal Identities  \n• sin  = ~~ ~~csc1~~ ~~~~ ~~  \n• cos  = ~~ ~~sec1~~ ~~~~ ~~  \n• tan  = ~~ ~~cot~~ ~~1~~ ~~~~ ~~  \nPhytagorean Identities  \n• sin2  cos2  = 1  \n• 1  tan2  = sec2   \n• 1  cot2  = csc2   \nCo-function Identities  \nDouble Angle Identities  \n• sin  2  = 2 sin  cos   \n• cos  2  = cos2  ~~ ~~ sin2  \n• cos  2  = 2 cos2  ~~ ~~ 1  \n• cos  2  = 1 ~~ ~~ 2 sin2   \n• tan  2  = ~~ ~~1~~ ~~2~~ ~~tantan2~~ ~~  \nNegative Angle Identities Supplement Angle Identities  \n• sin  ~~ ~~  = ~~ ~~ sin  • sin  ~~ ~~  = sin   \n• cos  ~~ ~~  = cos  • cos  ~~ ~~  = ~~ ~~ cos   \n• tan  ~~ ~~  = ~~ ~~ tan  • tan  ~~ ~~  = ~~ ~~ tan   \n• csc  ~~ ~~  = ~~ ~~ csc  • csc  ~~ ~~  = csc •  \n• sec  ~~ ~~  = sec   \n• cot  ~~ ~~  = ~~ ~~ cot   \nAngle Sum & Difference Identities  \n• sin  = sin  cos   cos  sin   \n• cos  = cos  cos   sin  sin   \n• tan  = ~~ ~~1~~ ~~tantan~~ ~~~~ ~~tantan~~ ~~~~ ~~  \nSum Identities  \n• sin  sin   \n= 2 sin  cos ~~ ~~~~ ~~  \n2 2  \n• sin  ~~ ~~ sin   \n= 2 cos  sin ~~ ~~~~ ~~  \n2 2  \n• cos   cos   \n= 2 cos  cos ~~ ~~~~ ~~  \n2 2  \n• cos  ~~ ~~ cos  =  \n~~ ~~ 2 sin  cos ~~ ~~~~ ~~  \n2 2  \n• sec  ~~ ~~  = ~~ ~~ sec   \n• cot  ~~ ~~  = ~~ ~~ cot   \nHalf-Angle Identities  \n• sin  =   1  cos    \n2 2  \n• cos  =   1  cos    \n2 2  \n• tan  ~~ ~~  =  sin   \n2 1  cos   \n• tan  =  1  cos    \n2 sin   \nProduct Identities  \n• sin  cos  = ~~ ~~12~~ ~~  sin  sin   \n• cos  sin  = ~~ ~~12~~ ~~  sin  ~~ ~~ sin   \n• cos  cos  = ~~ ~~12~~ ~~  cos  cos   \n• sin  sin  = ~~ ~~12~~ ~~  cos  ~~ ~~ cos","cbCailKcBmsfPlKu","https://ap.wps.com/l/cbCailKcBmsfPlKu","pdf",273225,"English","# Quotient and Reciprocal Identities\n## Pythagorean and Co-function Identities\n# Double Angle Identities\n## Half-Angle Identities\n# Angle Sum and Difference Identities\n## Sum and Product Identities\n# Negative and Supplement Angle Identities","[{\"question\":\"What are the three Pythagorean identities listed?\",\"answer\":\"The listed Pythagorean identities are sin^2θ + cos^2θ = 1, 1 + tan^2θ = sec^2θ, and 1 + cot^2θ = csc^2θ.\"},{\"question\":\"How is the double angle identity for sine expressed?\",\"answer\":\"The double angle identity for sine is expressed as sin(2θ) = 2 sin(θ) cos(θ).\"},{\"question\":\"What do negative angle identities tell us about cosine?\",\"answer\":\"Negative angle identities show that cos(-θ) = cos(θ), indicating that the cosine function is an even function.\"}]","Trigonometric Identities - Cheat Sheet | PDF",1791914545]