# Precalculus Examples

Step 1

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

Step 2

Find the amplitude .

Amplitude:

Step 3

Step 3.1

The period of the function can be calculated using .

Step 3.2

Replace with in the formula for period.

Step 3.3

The absolute value is the distance between a number and zero. The distance between and is .

Step 3.4

Cancel the common factor of and .

Step 3.4.1

Factor out of .

Step 3.4.2

Cancel the common factors.

Step 3.4.2.1

Factor out of .

Step 3.4.2.2

Cancel the common factor.

Step 3.4.2.3

Rewrite the expression.

Step 4

Step 4.1

The phase shift of the function can be calculated from .

Phase Shift:

Step 4.2

Replace the values of and in the equation for phase shift.

Phase Shift:

Step 4.3

Multiply the numerator by the reciprocal of the denominator.

Phase Shift:

Step 4.4

Multiply .

Step 4.4.1

Multiply by .

Phase Shift:

Step 4.4.2

Multiply by .

Phase Shift:

Phase Shift:

Phase Shift:

Step 5

List the properties of the trigonometric function.

Amplitude:

Period:

Phase Shift: ( to the right)

Vertical Shift: None

Step 6