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

`(2\pi)/(B)` - period

`- (C)/(B)` - phase shift


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

Amplitude: 5
Period:
`(2\pi)/(B)=(2\pi)/((1)/(2))=4\pi`
Phase shift:
`- (C)/(B) =- ((2\pi)/(3))/((1)/(2))= -(4\pi)/(3)`