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 .

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.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

Multiply by .

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 .

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.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

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.

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.

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.

Cancel the common factor of and .

Factor out of .

Cancel the common factors.

Factor out of .

Cancel the common factor.

Rewrite the expression.

Move to the left of .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because sine is negative in the fourth 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.

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 .

Move to the left of .

Subtract full rotations of until the angle is greater than or equal to and less than .

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 d=5sin(pi/4t)