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

• confident

• okay

• need practice

• confused