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 .
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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 .
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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.
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Calculate the point at .
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Replace the variable with in the expression.
Clarify the result.
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First, multiply by .
The exact value of is .
The result is .
Calculate the point at x=π .
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Replace the variable with in the expression.
Clarify the result.
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The common factor should be canceled of .
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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 .
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Replace the variable with in the expression.
Simplify the result.
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The common factor should be canceled.
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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 .
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Replace the variable with in the expression.
Simplify the result.
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Add and .
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 .
The final answer is .
Find the point at .
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Replace the variable with in the expression.
Simplify the result.
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Cancel the common factor of .
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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 .
The final answer is .
List the points in a table.
Use the amplitude to plot the trig function, period, phase shift, vertical shift, and the points.
Amplitude:
Period:
Phase Shift: ( to the right)
Vertical Shift:
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