[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-572239-105":3,"detail-sidebar-cat-1-en-105":72,"doc-detail-572239-en":118},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":65,"head_meta":67,"extra_data":69,"updated_unix":71},105,"en","trigonometric-identities-read-online-free","Trigonometric Identities - read online free","","Trigonometric Identities is a mathematics learning workbook designed to help readers learn and revise trigonometric identities through guided practice. It explains relationships among sin, cos, tan, sec, csc, and cot, including how identities differ from equations, and it demonstrates techniques to simplify and verify expressions. The material introduces key identities such as the Pythagorean identity sin^2θ+cos^2θ=1, angle-sum and angle-difference forms, double-angle formulae, and applications, reinforced by a pretest, exercises, self-assessment, and solution guidance.",{"@graph":14,"@context":64},[15,34,55],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/template/","Template",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/template/paper-templates/","Paper Templates",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/template/trigonometric-identities-read-online-free/572239/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/trigonometric-identities-read-online-free/572239.png","ImageObject",442,249,{"name":42,"@type":43},"Blitz","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-15","2026-10-13",true,{"@type":52,"interactionType":53,"userInteractionCount":22},"InteractionCounter",{"@type":54},"ViewAction",{"@type":56,"mainEntity":57},"FAQPage",[58],{"name":59,"@type":60,"acceptedAnswer":61},"Which key identity involving sin and cos is central to the workbook?","Question",{"text":62,"@type":63},"The workbook highlights the Pythagorean identity sin^2θ + cos^2θ = 1 and derives related results such as 1 + tan^2θ = sec^2θ and cot^2θ + 1 = csc^2θ.","Answer","https://schema.org",{"og:url":32,"og:type":66,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":68,"canonical":32},"index,follow",{"doc_id":70,"site_id":7},572239,1792053088,{"code":4,"msg":73,"data":74},"success",[75,80,85,90,95,100,105,110,114],{"id":76,"doc_module":22,"doc_module_name":25,"category_name":77,"show_sort_weight":78,"slug":79},11,"Presentations",90,"presentations",{"id":81,"doc_module":22,"doc_module_name":25,"category_name":82,"show_sort_weight":83,"slug":84},12,"Resumes",80,"resumes",{"id":86,"doc_module":22,"doc_module_name":25,"category_name":87,"show_sort_weight":88,"slug":89},14,"Invoices",70,"invoices",{"id":91,"doc_module":22,"doc_module_name":25,"category_name":92,"show_sort_weight":93,"slug":94},15,"Posters",60,"posters",{"id":96,"doc_module":22,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},16,"Social Media",50,"social-media",{"id":101,"doc_module":22,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},17,"Forms",40,"forms",{"id":106,"doc_module":22,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},18,"Letters",30,"letters",{"id":111,"doc_module":22,"doc_module_name":25,"category_name":29,"show_sort_weight":112,"slug":113},21,5,"papers-templates",{"id":115,"doc_module":22,"doc_module_name":25,"category_name":116,"show_sort_weight":4,"slug":117},158,"General","general-158",{"code":4,"msg":73,"data":119},{"doc_id":70,"user_id":120,"nickname":42,"user_avatar":121,"doc_module":22,"category_id":111,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":122,"file_id":123,"file_url":124,"file_type":125,"file_size":126,"view_count":22,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":106,"language":127,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":128,"faqs":129,"seo_title":130,"seo_description":12,"update_tm":131,"read_time":132},24464137899374,"https://us-avatar.wpscdn.com/davatar_3d24733baf745e90a7e4bdd5f77d97b2","Trigonometric Identities  \nPeggy Adamson  \nMathematics Learning Centre University of Sydney NSW 2006  \n􀀂c1986 University of Sydney  \nContents  \n1 Introduction 1  \n1.1 How to use this book .............................. 1  \n1.2 Introduction ................................... 1  \n1.3 Objectives .................................... 1  \n1.4 Pretest ...................................... 2  \n2 Relations between the trigonometric functions 2  \n3 The Pythagorean identities 4  \n4 Sums and differences of angles 7  \n5 Double angle formulae 11  \n6 Applications of the sum, difference, and double angle formulae 12  \n7 Self assessment 13  \n8 Solutions to exercises 14  \nMathematics Learning Centre, University of Sydney 1  \n1 Introduction  \n1.1 How to use this book  \nYou will not gain much by just reading this booklet. Have pencil and paper ready to work through the examples before reading their solutions. Do all the exercises. It is important that you try hard to complete the exercises on your own, rather than refer to the solutions as soon as you are stuck.  \n1.2 Introduction  \nThis unit is designed to help you learn, or revise, trigonometric identities.  \nYou need to know these identities, and be able to use them confidently. They are used in many different branches of mathematics, including integration, complex numbers and mechanics.  \nThe best way to learn these identities is to have lots of practice in using them. So weremind you of what they are, then ask you to work through examples and exercises. We’ve tried to select exercises that might be useful to you later, in your calculus unit of study.  \n1.3 Objectives  \nBy the time you have worked through this workbook you should  \n• be familiar with the trigonometric functions sin, cos, tan, sec, csc and cot, and with the relationships between them,  \n• know the identities associated with sin2 θ + cos2 θ = 1,  \n• know the expressions for sin, cos, tan of sums and differences of angles,  \n• be able to simplify expressions and verify identities involving the trigonometric functions,• know how to differentiate all the trigonometric functions,  \n• know expressions for sin 2θ, cos 2θ, tan 2θ and use them in simplifying trigonometric functions,  \n• know how to reduce expressions involving powers and products of trigonometric functions to simple forms which can be integrated.  \nMathematics Learning Centre, University of Sydney 2  \n1.4 Pretest  \nWe shall assume that you are familiar with radian measure for angles, and with the definitions and properties of the trigonometric functions sin, cos, tan. This test is included to help you check how well you remember these.  \n1. Express in radians angles of  \ni. 60◦ ii. 135◦ iii. 270◦  \n2. Express in degrees angles of π   3π  \ni. ii. − iii. 2π 4 2  \n3. What are the values of  \nπ   3π   3π  \ni. sin ii. cos iii. tan  \n2 2 4 7π   5π  \niv. sin V. cos vi. tan 2π 6 3  \n4. Sketch the graph of y = cos x.  \n2 Relations between the trigonometric functions  \nRecall the definitions of the trigonometric functions by means of the unit circle, x2 + y 2 = 1 .  \nsin θ = cos θ = tan θ =  \ny  \nx  \ny x  \nThree more functions are defined in terms of these, secant (sec), cosecant (cosec or csc) and cotangent (cot) .  \n 1   \nsec θ = (1)  \ncos θ  \n 1   \ncsc θ = (2)  \nsin θ  \n 1   \ncot θ = (3)  \ntan θ  \nMathematics Learning Centre, University of Sydney 3  \nThe functions cos and sin are the basic ones. Each of the others can be expressed in terms of these. In particular  \ntan θ = ~~ ~~sincosθθ~~ ~~ (4)  \ncos θ  \ncot θ = (5)  \nsin θ  \nThese relationships are identities, not equations. An equation is a relation between functions that is true only for some particular values of the variable.  \nπ  \nFor example, the relation sin θ = cos θ is an equation, since it is satisfied when θ = 4 , but not for other values of θ between 0 and π .  \nsin θ  \nOn the other hand, tan θ = is true for all values of θ, so this is an identity.  \ncos θ  \nThe relationships (1) to (5) above are true for all values of θ","cbCaioJ8BIvezZwM","https://ap.wps.com/l/cbCaioJ8BIvezZwM","pdf",667830,"English","# Contents\n## Introduction\n## Relations between the trigonometric functions\n## The Pythagorean identities\n## Sums and differences of angles\n## Double angle formulae\n## Applications of the sum, difference, and double angle formulae\n## Self assessment\n## Solutions to exercises","[{\"question\":\"Which key identity involving sin and cos is central to the workbook?\",\"answer\":\"The workbook highlights the Pythagorean identity sin^2θ + cos^2θ = 1 and derives related results such as 1 + tan^2θ = sec^2θ and cot^2θ + 1 = csc^2θ.\"}]","Trigonometric Identities - read online free | PDF",1791926319,6]