[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-1-en-105":3,"doc-seo-572237-105":53,"doc-detail-572237-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","trigformulas-trigonometric-formulas","TrigFormulas - Trigonometric Formulas","","A concise reference sheet for Calculus II trigonometric identities, including basic relations for sin(θ), cos(θ), and their derived functions tan, cot, sec, and csc. It presents addition formulas for sin(A+B) and cos(A+B), derives double-angle formulas, and includes integration-oriented transformations such as tan²(θ)+1=sec²(θ). The document also lists key derivative results and corresponding integral antiderivatives involving sin(x), sec(x), csc(x), and cot(x), using standard constant-of-integration notation.",{"@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/trigformulas-trigonometric-formulas/572237/",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/trigformulas-trigonometric-formulas/572237.png","ImageObject",442,249,{"name":88,"@type":89},"Mary Man","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 are the basic identities connecting sin(θ) and cos(θ)?","Question",{"text":108,"@type":109},"The sheet states sin(−θ)=−sin(θ), cos(−θ)=cos(θ), and sin²(θ)+cos²(θ)=1, with tan, cot, sec, and csc defined in terms of sin and cos.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"How are addition formulas used to obtain double-angle formulas?",{"text":113,"@type":109},"By setting A=B in the addition formulas for sin(A+B) and cos(A+B), the document derives sin(2A)=2sin(A)cos(A) and cos(2A)=cos²(A)−sin²(A), plus alternate rewritten forms.",{"name":115,"@type":106,"acceptedAnswer":116},"Which derivative and integral formulas are provided for common trigonometric functions?",{"text":117,"@type":109},"It gives derivatives like (sin x)'=cos x and (sec x)'=sec x tan x, and provides integrals such as ∫sin x dx=−cos x+C, ∫sec x dx=ln|sec x+tan x|+C, and ∫csc x dx=ln|csc x−cot x|+C.","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},572237,1792057079,{"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":9,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":4},7421720224475,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","MATH 10560: CALCULUS II  \nTRIGONOMETRIC FORMULAS  \nBasic Identities  \nThe functions cos(θ) and sin(θ) are defined to be the x and y coordinates of the point at an angle of θ on the unit circle. Therefore, sin(−θ) = −sin(θ), cos(−θ) = cos(θ), and sin2 (θ) + cos2 (θ) = 1 . The other trigonometric functions are defined in terms of sine and cosine:  \ntan(θ) = sin(θ)/cos(θ) cot(θ) = cos(θ)/sin(θ) = 1/tan(θ)  \nsec(θ) = 1/cos(θ) csc(θ) = 1/sin(θ)  \nDividing sin2 (θ) + cos2 (θ) = 1 by cos2 (θ) or sin2 (θ) gives tan2 (θ) + 1 = sec2 (θ) and 1 + cot2 (θ) = csc2 (θ) .  \nAddition Formulas  \nThe following two addition formulas are fundamental:  \nsin(A + B) = sin(A)cos(B) + cos(A)sin(B)  \ncos(A + B) = cos(A)cos(B) − sin(A)sin(B)  \nThey can be used to prove simple identities like sin(π/2 − θ) = sin(π/2)cos(θ)+ cos(π/2)sin(θ) = cos(θ), or cos(x − π) = cos(x)cos(π) − sin(x)sin(π) = −cos(x) . If we set A = B in the addition formulas we get the double-angle formulas:  \nsin(2A) = 2sin(A)cos(A) cos(2A) = cos2 (A) − sin2 (A)  \nThe formula for cos(2A) is often rewritten by replacing cos2 (A) with 1 − sin2 (A) or replacing sin2 (A) with 1 − cos2 (A) to get  \ncos(2A) = 1 − 2sin2 (A) cos(2A) = 2cos2 (A) − 1  \nSolving for sin2 (A) and cos2 (A) yields identities important for integration:  \n2  1 2  1  \nsin (A) = (1 − cos(2A)) cos (A) = (1 + cos(2A))  \n2 2  \nThe addition formulas can also be combined to give other formulas important for integration:  \nsinAsinB = ~~ ~~12 [cos(A − B) − cos(A + B)]  \ncosA cos B = ~~ ~~12 [cos(A − B) + cos(A + B)]  \nsinAcosB = ~~ ~~12 [sin(A − B) + sin(A + B)]  \nDerivatives and Integrals  \nsin′(x) = cos(x) cos′(x) = −sin(x) tan′(x) = sec2 (x)  \nR sin(x) dx = −cos(x) + CR cos(x)dx = sin(x) + CR tan(x) dx = ln|sec(x)| + C  \nsec′(x) = sec(x)tan(x)  \ncsc′(x) = −csc(x)cot(x)  \ncot′(x) = −csc2 (x)  \nR sec(x) dx = ln|sec(x) + tan(x)| + CR csc(x) dx = ln|csc(x) − cot(x)| + CR cot(x) dx = −ln|csc(x)| + C","cbCaihZM2peEg9mS","https://ap.wps.com/l/cbCaihZM2peEg9mS","pdf",24390,"English","# Basic Identities\n# Addition Formulas\n## Double-Angle Formulas\n# Derivatives and Integrals","[{\"question\":\"What are the basic identities connecting sin(θ) and cos(θ)?\",\"answer\":\"The sheet states sin(−θ)=−sin(θ), cos(−θ)=cos(θ), and sin²(θ)+cos²(θ)=1, with tan, cot, sec, and csc defined in terms of sin and cos.\"},{\"question\":\"How are addition formulas used to obtain double-angle formulas?\",\"answer\":\"By setting A=B in the addition formulas for sin(A+B) and cos(A+B), the document derives sin(2A)=2sin(A)cos(A) and cos(2A)=cos²(A)−sin²(A), plus alternate rewritten forms.\"},{\"question\":\"Which derivative and integral formulas are provided for common trigonometric functions?\",\"answer\":\"It gives derivatives like (sin x)'=cos x and (sec x)'=sec x tan x, and provides integrals such as ∫sin x dx=−cos x+C, ∫sec x dx=ln|sec x+tan x|+C, and ∫csc x dx=ln|csc x−cot x|+C.\"}]","TrigFormulas - Trigonometric Formulas | PDF",1791926314]