# How do you graph and list the amplitude, period, phase shift for y=cos((3x)/4)-4?

Jul 18, 2018

As below.

#### Explanation:

$y = \cos \left(\left(\frac{3}{4}\right) x\right) - 4$

Standard form of a cosine function is $y = A \cos \left(B x - C\right) + D$

$A = 1 , B = \frac{3}{4} , C = 0 , D = - 4$

$A m p l i t u \mathrm{de} = | A | = 1$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{\frac{3}{4}} = \frac{8 \pi}{3}$

$\text{Phase Shift } = \frac{- C}{B} = 0$

$\text{Vertical Shift } = D = - 4$

graph{cos ((3/4)x) - 4 [-10, 10, -5, 5]}