[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-523520-105":59,"doc-detail-523520-en":130},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","fundamental-trig-identities-use-identities-to-find-the-value-of-each-expression","Fundamental Trig Identities - Use identities to find the value of each expression","","Fundamental Trigonometric Identities worksheets for Infinite Precalculus practice include multiple problems where identities are used to determine missing trig function values such as sin, cos, tan, cot, sec, and csc. The set progresses through “If” statements that specify one or more trig expressions and asks for the corresponding complementary function values. The second part verifies trig identities by applying algebraic simplification and common-factor cancellation to confirm equality.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/fundamental-trig-identities-use-identities-to-find-the-value-of-each-expression/523520/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/fundamental-trig-identities-use-identities-to-find-the-value-of-each-expression/523520.png","ImageObject",300,407,{"name":92,"@type":93},"dhado","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-10","2026-10-08",true,{"@type":102,"interactionType":103,"userInteractionCount":52},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What is the purpose of the problems in this worksheet?","Question",{"text":112,"@type":113},"The worksheet uses fundamental trigonometric identities to find missing values of trig functions and to verify given identities.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"Which trigonometric functions are included?",{"text":117,"@type":113},"The problems use sin, cos, tan, cot, sec, and csc throughout both the value-finding and identity-verification sections.",{"name":119,"@type":110,"acceptedAnswer":120},"How do you handle the “Verify each identity” questions?",{"text":121,"@type":113},"Apply the relevant identities, simplify expressions, and cancel common factors to show both sides are equal.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},523520,1791629215,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":52,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":19,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":52,"preview_page_count":4},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Kuta Software-Infinite Precalculus Name   \nFundamental Trig Identities Date  Period   \nUse identities to find the value of each expression.  \n1) If sin 􀁔 􀀠 􀀐􀀓􀀑􀀜􀀖 , find cos ( 􀁔 􀀐 ~~ ~~) . 2) If tan (􀀐􀁔) 􀀠 􀀐􀀔􀀑􀀗􀀛 , find cot (~~ ~~~~ ~~ 􀀐 􀁔) .  \n3) If cos ( 􀁔 􀀐 ~~ ~~) 􀀠 􀀐􀀓􀀑􀀘􀀕 , find sin 􀁔 . 4) If sin 􀁔 􀀠 􀀓􀀑􀀔􀀙, find cos (~~ ~~~~ ~~ 􀀐 􀁔) .  \n5) If sec 􀁔 􀀠 􀀗􀀑􀀗􀀘 , find csc (~~ ~~~~ ~~ 􀀐 􀁔) . 6) If sin ( 􀁔 􀀐 ~~ ~~) 􀀠 􀀐􀀓􀀑􀀕􀀕 , find cos (􀀐􀁔) .  \n7) If tan 􀁔 􀀠 􀀐􀀓􀀑􀀛􀀚, find cot (~~ ~~~~ ~~ 􀀐 􀁔) . 8) If csc (~~ ~~~~ ~~ 􀀐 􀁔) 􀀠 􀀐􀀔􀀑􀀔􀀔 , find sec (􀀐􀁔) .  \n9) Find sin 􀁔 and sec 􀁔 10) Find csc 􀁔 and sin 􀁔 if tan 􀁔 􀀠 􀀖 and cos 􀁔 􀀟 􀀓 . if tan 􀁔 􀀠 􀀚􀀗 and sin 􀁔 􀀟 􀀓 .  \n11) Find cos 􀁔 and csc 􀁔 12) Find csc 􀁔 and sec 􀁔 if tan 􀁔 􀀠 􀀐 ~~ ~~􀀖􀀕 and sin 􀁔 􀀟 􀀓 . if cot 􀁔 􀀠 􀀖􀀕 and cos 􀁔 􀀡 􀀓 .  \n13) Find cot 􀁔 and cos 􀁔 14) Find cos 􀁔 and sec 􀁔 if csc 􀁔 􀀠 􀀘􀀕~~ ~~ and cos 􀁔 􀀟 􀀓 . if sin 􀁔 􀀠 􀀐 ~~ ~~􀀔􀀗 and cos 􀁔 􀀟 􀀓 .  \n15) Find csc 􀁔 and sin 􀁔 16) Find cos 􀁔 and sec 􀁔 if tan 􀁔 􀀠 􀀐  􀀕  and csc 􀁔 􀀟 􀀓 if cot 􀁔 􀀠 􀀐  􀀔  and cos 􀁔 􀀡 􀀓  \n􀀖 . 􀀕 .  \nVerify each identity.  \n17) sin xsec x 􀀠 tan x 18) sin~~ ~~x􀀔cot~~ ~~x 􀀠 co~~ ~~x  \n19) sec 􀀕 x 􀀐 csc 􀀕 x 􀀠 tan 􀀕 x 􀀐 cot 􀀕 x  \n20) csc 􀀕 xcos􀀕 x 􀀠 csc 􀀕 x 􀀐 􀀔  \nKuta Software-Infinite Precalculus Name   \nFundamental Trig Identities Date  Period   \nUse identities to find the value of each expression.  \n1) If sin 􀁔 􀀠 􀀐􀀓􀀑􀀜􀀖 , find cos ( 􀁔 􀀐 ~~ ~~) . 2) If tan (􀀐􀁔) 􀀠 􀀐􀀔􀀑􀀗􀀛 , find cot (~~ ~~~~ ~~ 􀀐 􀁔) .  \n􀀐􀀓􀀑􀀜􀀖 􀀔􀀑􀀗􀀛  \n3) If cos ( 􀁔 􀀐 ~~ ~~) 􀀠 􀀐􀀓􀀑􀀘􀀕 , find sin 􀁔 . 4) If sin 􀁔 􀀠 􀀓􀀑􀀔􀀙, find cos (~~ ~~~~ ~~ 􀀐 􀁔) .  \n􀀐􀀓􀀑􀀘􀀕 􀀓􀀑􀀔􀀙  \n5) If sec 􀁔 􀀠 􀀗􀀑􀀗􀀘 , find csc (~~ ~~~~ ~~ 􀀐 􀁔) . 6) If sin ( 􀁔 􀀐 ~~ ~~) 􀀠 􀀐􀀓􀀑􀀕􀀕 , find cos (􀀐􀁔) .  \n􀀗􀀑􀀗􀀘 􀀓􀀑􀀕􀀕  \n7) If tan 􀁔 􀀠 􀀐􀀓􀀑􀀛􀀚, find cot (~~ ~~~~ ~~ 􀀐 􀁔) . 8) If csc (~~ ~~~~ ~~ 􀀐 􀁔) 􀀠 􀀐􀀔􀀑􀀔􀀔 , find sec (􀀐􀁔) .  \n􀀐􀀓􀀑􀀛􀀚 􀀐􀀔􀀑􀀔􀀔  \n9) Find sin 􀁔 and sec 􀁔 if tan 􀁔 􀀠 􀀖 and cos 􀁔 􀀟 􀀓 .  \n􀀐 ~~ ~~􀀖~~ ~~􀀔~~ ~~􀀔􀀓~~ ~~􀀓~~ ~~ and 􀀐 􀀔􀀓  \n11) Find cos 􀁔 and csc 􀁔 if tan 􀁔 􀀠 􀀐 ~~ ~~􀀖􀀕 and sin 􀁔 􀀟 􀀓 .  \n 􀀕 􀀔􀀖   􀀔􀀖  and 􀀐  \n􀀔􀀖 􀀖  \n13) Find cot 􀁔 and cos 􀁔 if csc 􀁔 􀀠 􀀘􀀕~~ ~~ and cos 􀁔 􀀟 􀀓 .  \n􀀐 ~~ ~~􀀕􀀔􀀕~~ ~~ and 􀀐 ~~ ~~􀀕􀀔􀀘~~ ~~  \n15) Find csc 􀁔 and sin 􀁔 if tan 􀁔 􀀠 􀀐 ~~ ~~􀀕􀀖~~ ~~ and csc 􀁔 􀀟 􀀓 .  \n􀀐 ~~ ~~􀀔􀀖􀀕~~ ~~ and 􀀐 ~~ ~~􀀕~~ ~~􀀔􀀔􀀖~~ ~~􀀖~~ ~~  \n10) Find csc 􀁔 and sin 􀁔 if tan 􀁔 􀀠 􀀚􀀗 and sin 􀁔 􀀟 􀀓 .  \n􀀐 ~~ ~~􀀙􀀘􀀚~~ ~~ and 􀀐 ~~ ~~􀀚~~ ~~􀀙~~ ~~􀀙􀀘~~ ~~  \n12) Find csc 􀁔 and sec 􀁔  \nif cot 􀁔 􀀠  􀀖  and cos 􀁔 􀀡 􀀓􀀕 .  \n 􀀔􀀖   􀀔􀀖  and 􀀕 􀀖  \n14) Find cos 􀁔 and sec 􀁔 if sin 􀁔 􀀠 􀀐 ~~ ~~􀀔􀀗 and cos 􀁔 􀀟 􀀓 .  \n􀀐 ~~ ~~􀀔􀀘􀀗~~ ~~ and 􀀐 ~~ ~~􀀗~~ ~~􀀔~~ ~~􀀘􀀔~~ ~~  \n16) Find cos 􀁔 and sec 􀁔 if cot 􀁔 􀀠 􀀐 ~~ ~~􀀔􀀕~~ ~~ and cos 􀁔 􀀡 􀀓 .  \n~~ ~~􀀘~~ ~~ and   \nVerify each identity.  \n17) sin xsec x 􀀠 tan x  \nsin xsec x Use sec x 􀀠 ~~ ~~co~~ ~~x  \n sin x  \ncos x  \ntan x  \nsin x  \nUse tan x 􀀠 ~~  ~~cos x  \n■  \n18)  􀀔  􀀠  􀀔  sin xcot x cos x  \n 􀀔   cos x Use cot x 􀀠  \nsin xcot x sin x  \n sin x   \nCancel common factors sin xcos x  \n 􀀔   \n■ cos x  \n19) sec 􀀕 x 􀀐 csc 􀀕 x 􀀠 tan 􀀕 x 􀀐 cot 􀀕 x  \nsec 􀀕 x 􀀐 csc 􀀕 x Use cot􀀕 x 􀀎 􀀔 􀀠 csc􀀕 x  \nsec 􀀕 x 􀀐 cot 􀀕 x 􀀐 􀀔  \ntan 􀀕 x 􀀐 cot 􀀕 x  \nUse tan􀀕 x 􀀎 􀀔 􀀠 sec􀀕 x  \n■  \n20) csc 􀀕 xcos􀀕 x 􀀠 csc 􀀕 x 􀀐 􀀔  \ncsc 􀀕 xcos􀀕 x Use csc x 􀀠 ~~ ~~si~~ ~~x  \ncos 􀀕 x  \nsin 􀀕 x cot 􀀕 x  \ncsc 􀀕 x 􀀐 􀀔  \nUse cot x 􀀠  cos x sin x  \nUse cot􀀕 x 􀀎 􀀔 􀀠 csc􀀕 x  \n■  \nCreate your own worksheets like this one with Infinite Precalculus. Free trial available [at KutaSoftware.com](at KutaSoftware.com)","cbCaijPeqxHUN85M","https://ap.wps.com/l/cbCaijPeqxHUN85M","pdf",83656,"English","# Use identities to find the value of each expression\n## Verify each identity","[{\"question\":\"What is the purpose of the problems in this worksheet?\",\"answer\":\"The worksheet uses fundamental trigonometric identities to find missing values of trig functions and to verify given identities.\"},{\"question\":\"Which trigonometric functions are included?\",\"answer\":\"The problems use sin, cos, tan, cot, sec, and csc throughout both the value-finding and identity-verification sections.\"},{\"question\":\"How do you handle the “Verify each identity” questions?\",\"answer\":\"Apply the relevant identities, simplify expressions, and cancel common factors to show both sides are equal.\"}]","Fundamental Trig Identities - Use identities to find the value of each expression | PDF",1791426948]