# Graph f(x)=-3/2*sin(x)

Graph f(x)=-3/2*sin(x)
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 of .
The period of the function can be calculated using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
Divide by .
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:
Divide 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:
Select a few points to graph.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
The exact value of is .
Multiply by .
Divide by .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.
The exact value of is .
Simplify the expression.
Multiply by .
Divide by .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth quadrant.
The exact value of is .
Multiply by .
Simplify the expression.
Multiply by .
Move the negative in front of the fraction.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Simplify the expression.
Multiply by .
Divide by .
Multiply by .