Trigonometric Sum and Difference Identities

Sum and Difference Identities

Objectives

• We will be able to expand a trig expression by applying the sum or difference identity of that trig function.

• We will be able to condense the expanded form of the sum or difference identity.

• We will be able to evaluate the sin, cos, or tan of unfamiliar angles using the sum of difference of familiar angles.

Multiple Choice

Evaluate  $$\cos60\degree$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\sqrt{2}}{2}$$  

• 1

Multiple Choice

Evaluate $$\sin360\degree$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\sqrt{2}}{2}$$  

• $$\frac{1}{2}$$  

• 0

Sum and Difference Identities

Sine

Sum and Difference Identities

Cosine

Multiple Choice

Which of the following is the same as $$\cos\ \left(A+B\right)$$  

• $$\sin A\cos\ B\ +\ \cos\ A\ \sin\ B$$  

• $$\sin\ A\ \cos\ B\ -\ \cos\ A\ \sin\ B$$  

• $$\cos\ A\ \cos\ B\ +\ \sin\ A\ \sin\ B$$  

• $$\cos\ A\ \cos\ B\ -\ \sin\ A\ \sin\ B$$  

Sum and Difference Identities

Tangent

Multiple Choice

Which of the following is equivalent to $$\tan\ \left(A-B\right)$$  

• $$\tan\ A\ -\ \tan\ B$$  

• $$\frac{\tan\ A\ -\tan\ B}{1+\ \tan A\tan B}$$  

• $$\frac{\tan\ A\ +\tan\ B}{1-\ \tan A\tan B}$$  

• $$\frac{\sin\ A}{\cos\ B}$$  

Examples

•  $\sin105\degree$  

•  $\tan210\degree$  

•  $\cos\left(\frac{\pi}{3}+\frac{\pi}{6}\right)$  

•  $\sin\left(\frac{\pi}{2}-\frac{\pi}{6}\right)$  
  

•  $\tan\left(15\degree\right)$  

Multiple Choice

Expand $$\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$$  

• $$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$$  

• $$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$$  

• $$\cos\ \frac{2\pi}{11}$$  

• $$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$$  

Multiple Choice

$$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$$  is equivalent to

• $$\sin\ 90^{o\ }$$  

• $$\sin\ 60^{o\ }$$  

• $$\cos\ 90^{o\ }$$  

• $$\cos\ 60^{o\ }$$  

Poll

Gauge your understanding of today's lesson

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• okay

• need practice

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