# Graph y=9/4*cos(-1/3x)

Graph y=9/4*cos(-1/3x)
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 of .
The period of the function can be calculated using .
Replace with in the formula for period.
is approximately which is positive so remove the absolute value
Multiply the numerator by the reciprocal of the denominator.
Multiply 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:
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:
Select a few points to graph.
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
The exact value of is .
Multiply by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify the numerator.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
The exact value of is .
Simplify the expression.
Multiply by .
Divide by .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Cancel the common factor.
Divide by .
Simplify the numerator.
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because cosine is negative in the second 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.
Multiply the numerator by the reciprocal of the denominator.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
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 .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of and .
Factor out of .
Cancel the common factors.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Divide by .
Simplify the numerator.
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .