# Find Amplitude, Period, and Phase Shift y equals one divide two times cos(four x minus(two pi) divide three)

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

Calculate the amplitude .

Amplitude:

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:

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:

First, multiply the numerator by the denominator's reciprocal.

Phase Shift:

The common factor should be canceled.

Factor out of .

Phase Shift:

Factor out of .

Phase Shift:

Cancel the common factor.

Phase Shift:

Should be rewritten the expression.

Phase Shift:

Phase Shift:

Multiply and .

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:

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