Trig 3-7

Trig 3-7

Product-To-Sum, and Sum-To-Product Formulas

Multiple Choice

Quick Check 1

Express the product $\cos(3θ)\cos⁡(θ)$ as a sum containing only cosines. 

•  $\frac{1}{2}\left[\cos\left(\theta\right)+\cos\left(3\theta\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(2\theta\right)+\cos\left(4\theta\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(2\theta\right)-\cos\left(4\theta\right)\right]$  

•  $\frac{1}{2}\left[\sin\left(2\theta\right)-\cos\left(4\theta\right)\right]$  

Multiple Choice

Quick Check 2

Express the product  $\sin⁡(3θ)\cos⁡(5θ)$ as a sum.

•  $\frac{1}{2}\left[\sin\left(2\theta\right)-\sin\left(8\theta\right)\right]$  

•  $\frac{1}{2}\left[\cos\left(8\theta\right)-\sin\left(2\theta\right)\right]$  

•  $\frac{1}{2}\left[\sin\left(8\theta\right)-\sin\left(2\theta\right)\right]$  

•  $\frac{1}{2}\left[\sin\left(8\theta\right)+\sin\left(2\theta\right)\right]$  

Multiple Choice

Quick Check 3

Express the sum $\cos⁡(3θ)+\cos⁡(2θ)$  as a product of sines and cosines.

•  $2\cos\left(\frac{5\theta}{2}\right)\cos\left(\frac{\theta}{2}\right)$  

•  $2\sin\left(\frac{5\theta}{2}\right)\cos\left(\frac{\theta}{2}\right)$  

•  $2\cos\left(\frac{5\theta}{2}\right)\sin\left(\frac{\theta}{2}\right)$  

•  $2\sin\left(\frac{5\theta}{2}\right)\sin\left(\frac{\theta}{2}\right)$