Question

How do you find the period, amplitude and sketch `y=-4sin(2/3x-pi/3)`?

Answer 1

As below.

Explanation:

`y = -4 sin(2/3 x - pi/3)`

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

`A = -4, B = 2/3, C = pi/3, D = 0`

Amplitude `= |A| = |-4| = 4`

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

Phase Shift `= -C / B = (-pi/3) / (2/3) = -(pi/2), pi/2` to the LEFT.

Vertical Shift `= D = 0`

graph{-4 sin((2/3) x - (pi/3)) [-10, 10, -5, 5]}