# How do you find the period, amplitude and sketch y=3cos(x+pi)-3?

Mar 18, 2018

$A m p l i t u \mathrm{de} = 3 , P e r i o d = 2 \pi , \text{Phase Shift } = - \pi$

#### Explanation:

Given $y = 3 \cos \left(x + \pi\right) - 3$

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

$\text{Amplitude } = A = 3$

Period " = P = (2pi) / |B| = (2pi) / 1 = 2pi

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

$\text{Vertical Shift } = D = - 3$

graph{3 cos(x + pi) - 3 [-10, 10, -5, 5]}