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cos x bsin x Rcos(x α - University of Sheffield

Acosx+bsinx= Rcos(x )In this unit we explore how the sum of two trigonometric functions, 3 cosx+ 4 sinx, canbe expressed as a single trigonometric function. Having the ability to do this enables you tosolve certain sorts of trigonometric equations and find maximum and minimum values of sometrigonometric order to master the techniques explained here it is vital that you undertake the practiceexercises reading this text, and/or viewing the video tutorial on this topic, you should be able to: express the sum of two trigonometric functions,acosx+bsinx, in the formRcos(x ). use this technique to solve some equations. use this technique to locate maximum and minimum graph ofy= 3 cosx+ 4 expressionRcos(x ) the result to solve an maximum and minimum values71c mathcentreJune11,20041. IntroductionIn this unit we are going to have a look at a particular form of trigonometric function. Considerthe following function, which is a sum of two trigonometric functions:3 cosx+ 4 sinxYou will find that in some applications, for example in solving trigonometric equations, it ishelpful to write these two terms as a single term.

Key Point acosx+bsinx canbewrittenas Rcos(x−α) where R = a2 +b2, tanα = b a Thisisaveryusefultooltohaveatone’sdisposal. Itreducesthesumoftwotrigonometric ...

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