# How do you graph and list the amplitude, period, phase shift for y=3cos(1/2)x+4?

Jun 19, 2018

As below.

#### Explanation:

$y = A \cos \left(B x - C\right) + D$

$y = 3 \cos \left(\frac{x}{2}\right) + 4$

$A m p l i t u \mathrm{de} = | A | = 3$

$\text{Period } = \frac{2 \pi}{|} B | = \frac{2 \pi}{\frac{1}{2}} = 4 \pi$

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

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

graph{3 cos (x/2) + 4 [-10, 10, -5, 5]}