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

Cancel the common factor of .

Cancel the common factor.

Divide 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:

Cancel the common factor of .

Cancel the common factor.

Phase Shift:

Rewrite the expression.

Phase Shift:

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 .

Subtract from .

The exact value of is .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Combine and .

Move to the left of .

To write as a fraction with a common denominator, multiply by .

Combine fractions.

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

The exact value of is .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Move to the left of .

Subtract from .

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

The exact value of is .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

Combine and .

Move to the left of .

To write as a fraction with a common denominator, multiply by .

Combine fractions.

Combine and .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by .

Subtract from .

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 .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Move to the left of .

Subtract from .

Subtract 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.

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 sin(pi(x-1))