HPC Section 5.4 Sum and Difference Formulas Pt 1

PreCalculus Section 5.4

​Sum and Difference Formulas

Multiple Choice

True or False:

$$\cos\ \left(30\ +\ 45\right)\ =\ \cos\ \left(30\right)\ +\ \cos\ \left(45\right)$$  

• True

• False

Multiple Choice

True or False:

$$\cos\ \left(x\ +\ 2\right)\ =\ \cos\ \left(x\right)\ +\ \cos\ \left(2\right)$$  

• True

• False

Multiple Choice

You know the answer to this:  Think about the graph. 

What does this represent?
$$y\ =\cos\ \left(x\ +\ 2\right)\$$  

• Vertical Shift up

• Horizontal Shift right

• Vertical Shift down
  

• Horizontal shift left
  

Multiple Choice

You know the answer to this:  Think about the graph. 

What does this represent? (in radians)
$$y\ =\ \cos\ \left(x\right)\ +\ \cos\ \left(2\right)$$  

• Vertical Shift up
  

• Horizontal Shift right
  

• Vertical Shift down
  

• Vertical Shift left
  

These two graphs are NOT THE SAME!

It might be a good time to review this.

​

​

​

​

Draw

Solve

$$\cos\ 75\ =\ \cos u\cos v-\ \sin u\sin v$$

Draw

Solve

$$\tan\left(\frac{5\pi}{12}\right)=\frac{\tan u+\tan v}{1-\tan u\tan v}$$

Draw

Solve

$$\sin\left(\frac{\pi}{12}\right)=\sin u\cos v-\cos u\sin v$$

Multiple Select

Simplify and solve:
$$\cdot\cos78\degree\cos18\degree+\sin78\degree\sin18\degree=$$  

• $$\sin\left(60\degree\right)$$  

• $$\cos\left(60\degree\right)$$  

• $$\frac{1}{2}$$  

• $$\frac{\sqrt{3}}{2}$$  

• $$\frac{\sqrt{2}}{2}$$