# How do you graph y = 2 cos 3 (x - (pi/4))?

Jul 4, 2018

As below.

#### Explanation:

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

$\text{Given : } y = 2 \cos \left(3 x - \frac{3 \pi}{4}\right)$

$A = 2 , B = 3 , C = \frac{3 \pi}{4} , D = 0$

$A m p l i t u \mathrm{de} = | A | = 2$

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

$\text{Phase Shift " = -C / B = -((3pi)/4) / 3 = -(pi/4),color(crimson)( pi/4 " to the LEFT}$

$\text{Vertical Shift } = D = 0$

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