Question

What is the amplitude, period and the phase shift of `y = 3sin2x-(pi/2)`?

Answer 1

As below.

Explanation:

I assume the question to be `y = 3 sin(2x - pi/2)`

Standard form of a sine function is `y = A sin (Bx - C) + D`

`A = 3, B = 2, C = pi/2, D = 0`

`Amplitude = |A| = |3| = 3`

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

`"Phase Shift " = (-C) / B = (-pi/2) / 2 = -pi/4, color(crimson)(pi/4 " to the LEFT"`

`"Vertical Shift " = D = 0`

graph{3 sin(2x - pi/2) [-10, 10, -5, 5]}