# Find Amplitude, Period, and Phase Shift y=-2sin(2/3x)

Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period using the formula .
The period of the function can be calculated using .
Period:
Replace with in the formula for period.
Period:
Solve the equation.
is approximately which is positive so remove the absolute value
Period:
Multiply the numerator by the reciprocal of the denominator.
Period:
Cancel the common factor of .
Factor out of .
Period:
Cancel the common factor.
Period:
Rewrite the expression.
Period:
Period:
Move to the left of .
Period:
Period:
Period:
Find the phase shift using the formula .
The phase shift of the function can be calculated from .
Phase Shift:
Replace the values of and in the equation for phase shift.
Phase Shift:
Multiply the numerator by the reciprocal of the denominator.
Phase Shift:
Multiply by .
Phase Shift:
Phase Shift:
Find the vertical shift .
Vertical Shift:
List the properties of the trigonometric function.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
Find Amplitude, Period, and Phase Shift y=-2sin(2/3x)