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:

Multiply the numerator by the reciprocal of the denominator.

Period:

Multiply .

Combine and .

Period:

Multiply by .

Period:

Combine and .

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:

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:

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.

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 .

Reduce the expression by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Cancel the common factor.

Rewrite the expression.

Divide by .

The exact value of is .

Multiply by .

Divide by .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Combine and .

Multiply by .

Reduce the expression by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Simplify the numerator.

Cancel the common factor of .

Cancel the common factor.

Divide 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 .

Simplify the expression.

Multiply by .

Move the negative in front of the fraction.

The final answer is .

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 .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Combine and .

Multiply by .

Reduce the expression by cancelling the common factors.

Reduce the expression by cancelling the common factors.

Factor out of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Divide by .

Simplify the numerator.

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 .

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=4/3cos(3/2x)