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

Aug 2, 2018

As below.

#### Explanation:

I assume the question to be $y = 3 \sin \left(2 x - \frac{\pi}{2}\right)$

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

$A = 3 , B = 2 , C = \frac{\pi}{2} , D = 0$

$A m p l i t u \mathrm{de} = | A | = | 3 | = 3$

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

$\text{Phase Shift " = (-C) / B = (-pi/2) / 2 = -pi/4, color(crimson)(pi/4 " to the LEFT}$

$\text{Vertical Shift } = D = 0$

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