Question

What is the amplitude, period, and phase shift of y= 5cos( x/2 + 2pi/3)

Answer 1

Y = A cos(Bx + C)
A - amplitude
$\frac{2\pi}{B}$ - period
$- \frac{C}{B}$ - phase shift

$y=5\cos{( \frac{x}{2} + \frac{2\pi}{3} )} \\ \\y=5\cos{( \frac{1}{2}x + \frac{2\pi}{3})} \\ \\A=5,B= \frac{1}{2},C= \frac{2\pi}{3}$

Amplitude: 5
Period: $\frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi$
Phase shift: $- \frac{C}{B} =- \frac{\frac{2\pi}{3}}{\frac{1}{2}}= -\frac{4\pi}{3}$