Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.

Find the amplitude .

Amplitude:

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:

Cancel the common factor of .

Cancel the common factor.

Period:

Divide by .

Period:

Period:

Period:

Period:

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:

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

The exact value of is .

Multiply by .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Combine and .

The exact value of is .

Multiply by .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Multiply by .

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 .

Multiply by .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Combine and .

Move to the left of .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant.

The exact value of is .

Multiply by .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Move to the left of .

is a full rotation so replace with .

The exact value of is .

Multiply by .

The final answer is .

List the points in a table.

The trig function can be graphed using the amplitude, period, phase shift, vertical shift, and the points.

Amplitude:

Period:

Phase Shift: ( to the right)

Vertical Shift:

Graph y=4cos(pix)