Precalculus Examples

Find Amplitude, Period, and Phase Shift
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Find the amplitude .
Amplitude:
Find the period using the formula .
Tap for more steps...
The period of the function can be calculated using .
Period:
Replace with in the formula for period.
Period:
Solve the equation.
Tap for more steps...
The absolute value is the distance between a number and zero. The distance between and is .
Period:
Reduce the expression by cancelling the common factors.
Tap for more steps...
Cancel the common factor.
Period:
Divide by .
Period:
Period:
Period:
Period:
Find the phase shift using the formula .
Tap for more steps...
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:
Enter YOUR Problem
Mathway requires javascript and a modern browser.