# Graph y equals one divide two times sin(three x)

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 .

Replace with in the formula for period.

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

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, First, 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:

Calculate the point at .

Replace the variable with in the expression.

Clarify the result.

Clarify the numerator.

First, multiply by .

The exact value of is .

Divide by .

The result is .

Calculate the point at x=π .

Replace the variable with in the expression.

Clarify the result.

Simplify the numerator.

The common factor should be canceled of .

Factor out of .

Cancel the common factor.

Reformulate the expression.

The exact value of is .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

The common factor should be canceled.

Cancel the common factor.

Should be rewritten the expression.

Use the reference angle by calculating the angle with equivalent triginometric values in the Initially quadrant.

The exact value of is .

Divide by .

The final answer is .

Calculate the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

Add and .

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Rewrite the expression as a negative one since sine is negative in the 2nd quadrant.

The exact value of is .

Multiply by .

Put the negative in front of the fraction.

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify the numerator.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Subtract full rotations of until the angle is greater than or equal to and less than .

The exact value of is .

Divide by .

The final answer is .

List the points in a table.

Use the amplitude to plot the trig function, period, phase shift, vertical shift, and the points.

Amplitude:

Period:

Phase Shift: ( to the right)

Vertical Shift:

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