# What is the period and amplitude for y= -1/2cos(3x+4pi/3)?

May 30, 2018

$A m p l i t u \mathrm{de} = | A | = \frac{1}{2}$

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

#### Explanation:

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

Given $y = \left(\frac{1}{2}\right) \cos \left(3 x + \textcolor{c r i m s o n}{\frac{4 \pi}{3}}\right)$

$A = \frac{1}{2} , B = 3 , C = \frac{4 \pi}{3}$

$A m p l i t u \mathrm{de} = | A | = \frac{1}{2}$

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

Phase Shift $= - \frac{C}{B} = \frac{\frac{4 \pi}{3}}{3} = \frac{4 \pi}{9}$

Vertical Shift = D = 0#