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4.4 Compound Angle Formulas

__Compound Angle Formulas____For Cos__Cos(a-b) = Cos* a *Cos *b +* Sin *a *Sin *b*Cos(a+b) = Cos *a *Cos *b - *Sin *a *Sin *b*Notices that when the left half of the equation is a minus, the right half of the equation is plus. And vice versa.__For Sin__Sin(a-b) = Sin a Cos b - Cos a Sin bSin(a+b) = Sin *a* Cos *b* + Cos *a* Sin *b*And as for Sin the plus and minus sign stayed the same on both side. The difference with these two formulas is that here is Sin x Cos and Cos x Sin a mixture of sin and cos where as for Cos is only Cos x Cos and Sin x Sin.We use these four formulas to determine the exact value fo an angle.For example: cos( π/3 - π/4)**First we write out the whole equation:**Cos(π/3 - π/4) = Cos(π/3)Cos(π/4) + Sin(π/3)Sin(π/4)**Next we look at the exact value for Cos(π/3),Cos(π/4),Sin(π/3),Sin(π/4)****If we look at our special triangles we know that: Cos(π/3)is 1/2, Cos(π/4) is 1/√ 2, Sin(π/3) is √3/2, and Sin(π/4) is 1/√ 2, so now our new equation will be:**(1/2)(1/√ 2) + (√3/2)(1/√ 2)**Now we simplify it:**(1/2√ 2) + (√ 3/2√ 2)**which equals to:**1+√ 3/ 2√ 2Another example to use these equations will be express the formulas as a single trigonometric function.**example: Express as a single trigonometric function Sinπ Cosπ/4 + Cosπ Sin π/4****Equals: **Sin (π+ π/4) = Sin (5π/4)

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