# Graph cos(minus three x)

Graph cos(-3x)
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Calculate the amplitude .
Amplitude:
Calculate the period of .
Evaluate the period of function using .
Replace with in the formula for period.
The absolute value is the distance between a number and zero. The distance between and is .
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:
First, First, 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.
Calculate the point at .
Replace the variable with in the expression.
Clarify the result.
First, multiply by .
The exact value of is .
The result is .
Calculate the point at x=π .
Replace the variable with in the expression.
Clarify the result.
The common factor should be canceled of .
Factor out of .
Factor out of .
Cancel the common factor.
Reformulate the expression.
Should be rewritten as .
Add full rotations of until the angle is greater than or equal to and less than .
Use the reference angle by calculating the angle with equivalent triginometric values in the Initially quadrant.
The exact value of is .
The result is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
The common factor should be canceled.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Rewrite as .
Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Rewrite the expression as a negative one since cosine is negative in the 2nd quadrant.
The exact value of is .
Multiply by .
The result is .
Calculate the point at .
Replace the variable with in the expression.
Simplify the result.
Put the negative in front of the fraction.
Add full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
First, multiply by .
Add full rotations of until the angle is greater than or equal to and less than .
The exact value of is .