Question

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

Answer 1

`Amplitude = |A| = 1/2`

Period `= (2pi) / |B| = (2pi) / 3`

Explanation:

Standard form of the cos function is `y = A cos (Bx - C) + D`

Given `y = (1/2) cos (3x + color(crimson)((4pi)/3))`

`A = 1/2, B = 3, C = (4pi)/3`

`Amplitude = |A| = 1/2`

Period `= (2pi) / |B| = (2pi) / 3`

Phase Shift `= -C / B = ((4pi)/3) / 3 = (4pi)/9`

Vertical Shift = D = 0#