[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572240-105":53,"doc-detail-572240-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","21-trig-identities-every-calculus-student-should-know-reference-sheet","21 Trig Identities Every Calculus Student Should Know - Reference Sheet","","This document provides a comprehensive reference list of 21 essential trigonometric identities vital for success in calculus. The content is organized to include fundamental reciprocal and quotient identities, Pythagorean identities, sum and difference formulas for sine and cosine, and double-angle formulas. Additionally, the guide features two special right-triangle diagrams designed to assist students in quickly determining trigonometric functional values for common angles within the [0, 2π] interval, such as π/6, π/4, and π/3. By centralizing these core mathematical rules, the document serves as a high-utility study aid for students navigating complex calculus problems that require rapid trigonometric simplification and evaluation. It emphasizes practical application, ensuring that students can efficiently recall and apply these identities in both homework and examination settings to solve for specific angle values.",{"@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/21-trig-identities-every-calculus-student-should-know-reference-sheet/572240/",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/21-trig-identities-every-calculus-student-should-know-reference-sheet/572240.png","ImageObject",442,249,{"name":88,"@type":89},"Fans","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-22","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":101},"InteractionCounter",{"@type":100},"ViewAction",7,{"@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 identities are sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ, and cot²θ + 1 = csc²θ.","Answer",{"name":112,"@type":107,"acceptedAnswer":113},"How are reciprocal functions defined for sine and cosine?",{"text":114,"@type":110},"Cosecant (csc θ) is 1/sin θ and secant (sec θ) is 1/cos θ.",{"name":116,"@type":107,"acceptedAnswer":117},"How do the special triangles assist students?",{"text":118,"@type":110},"They allow students to quickly find trigonometric function values for common angles like 0, π/6, π/4, π/3, and π/2 within the [0, 2π] range.","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},572240,1792009227,{"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":9,"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":4},5909892330395,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","21 Trig Identities Every Calculus Student Should Know!  \n1. sin 􀀒 = cs1c~~ ~~􀀒  \n 1   \n[2. csc](2. csc) 􀀒 =  \nsin 􀀒  \n 1   \n3. cos 􀀒 =  \nsec 􀀒  \n 1   \n4. sec 􀀒 =  \ncos 􀀒  \nsin 􀀒   1   \n5.{ 6 . tan 􀀒 = =  \ncos 􀀒 cot 􀀒  \ncos 􀀒   1   \n7.{ 8 . cot 􀀒 = =  \nsin 􀀒 tan 􀀒  \n9. sin2 􀀒 + cos2 􀀒 = 1 (Pythagorean Identity)  \n10. tan2 􀀒 + 1 = sec2 􀀒  \n11. cot2 􀀒 + 1 = csc2 􀀒  \n12. sin(􀀋 + 􀀌) = sin 􀀋 cos 􀀌 + cos 􀀋 sin 􀀌  \n13. sin(􀀋 􀀀 􀀌) = sin 􀀋 cos 􀀌 􀀀 cos 􀀋 sin 􀀌  \n14. cos(􀀋 + 􀀌) = cos 􀀋 cos 􀀌 􀀀 sin 􀀋 sin 􀀌  \n15. cos(􀀋 􀀀 􀀌) = cos 􀀋 cos 􀀌 + sin 􀀋 sin 􀀌  \n16. sin 2􀀒 = 2 sin 􀀒 cos 􀀒  \n17.{19 . cos 2􀀒 = cos2 􀀒 􀀀 sin2 􀀒 = 2 cos2 􀀒 􀀀 1 = 1 􀀀 2 sin2 􀀒  \n20. cos2 􀀒 = 1~~ ~~+~~ ~~co2s~~ ~~2􀀒  \n21. sin2 􀀒 = 1 􀀀 cos 2􀀒  \n...........................................................................  \n. ...  \n2 . ...  \n. .... ...  \n. .... ...  \n......  \np3  \nTwo Special Triangles  \n..........................................................  \n. .... p2.................................................................................... ..............  \n. ..... ....  \n. ........  \n1  \n1  \n1  \nFrom the above two triangles you should be able to quickly 􀀌nd all extant trigonometic functional values of all the special angles 􀀒 in [0 ; 2􀀙] . I.e. ,􀀒 = 0; 􀀙=6; 􀀙=4; 􀀙=3; 􀀙=2 ; 2􀀙=3 ; : : : ; 2􀀙 . For example:  \nsin(3􀀙=4) = 1= p2  \nand    \ncot(5􀀙=3) = 􀀀1= p3 :","cbCaio2aN3c8SwZT","https://ap.wps.com/l/cbCaio2aN3c8SwZT","pdf",28847,"English","# Reciprocal and Quotient Identities\n## Pythagorean and Angle Identities\n# Special Triangles and Angle Values","[{\"question\":\"What are the three Pythagorean identities listed?\",\"answer\":\"The identities are sin²θ + cos²θ = 1, tan²θ + 1 = sec²θ, and cot²θ + 1 = csc²θ.\"},{\"question\":\"How are reciprocal functions defined for sine and cosine?\",\"answer\":\"Cosecant (csc θ) is 1/sin θ and secant (sec θ) is 1/cos θ.\"},{\"question\":\"How do the special triangles assist students?\",\"answer\":\"They allow students to quickly find trigonometric function values for common angles like 0, π/6, π/4, π/3, and π/2 within the [0, 2π] range.\"}]","21 Trig Identities Every Calculus Student Should Know - Reference Sheet | PDF",1791926323]