# How do you find the amplitude, period, vertical and phase shift and graph y=2/3cos(theta-50)?

Mar 8, 2018

Amplitude = 2/3, Period = $2 \pi$

Phase shift = 50 to the right, Vertical shift = 0

#### Explanation:

Standard form of equation $y = a \cos \left(b x - c\right) + d$

Where $A m p l i t u \mathrm{de} = a , P e r i o d = \frac{2 \pi}{|} b | , P h a s e$ shift $= - \frac{c}{b} , v e r t i c a l$ shift $= d$

Given equation is $y = \left(\frac{2}{3}\right) \cos \left(\theta - 50\right)$

Amplitude $= a = \left(\frac{2}{3}\right)$

Period $= \frac{2 \pi}{|} b | = \left(2 \pi\right)$

Phase shift = -c / b = 50# to the right

Vertical shift $= d = 0$

graph{(2/3) cos (x - 50) [-10, 10, -5, 5]}