# Find Amplitude, Period, and Phase Shift y equals three cos(ten(x minus pi))

Find Amplitude, Period, and Phase Shift y=3cos(10(x-pi))
Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift.
Calculate the amplitude .
Amplitude:
Calculate the period using the formula .
Evaluate the period of function using .
Period:
Replace with in the formula for period.
Period:
Find solution to the equation.
The absolute value is the distance between a number and zero. The distance between and is .
Period:
The common factor should be canceled of and .
Factor out of .
Period:
The common factors should be canceled.
Factor out of .
Period:
Cancel the common factor.
Period:
Reformulate the expression.
Period:
Period:
Period:
Period:
Period:
Find the phase shift using the formula .
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:
The common factor should be canceled.
Cancel the common factor.
Phase Shift:
First, divide by .
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:
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