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

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.

is approximately which is positive so remove the absolute value

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

First, multiply by .

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:

Multiply the numerator by the reciprocal of the denominator.

Phase Shift:

First, 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:

Calculate the point at .

Replace the variable with in the expression.

Clarify the result.

Clarify each term.

First, First, divide by .

The exact value of is .

Multiply by .

Sum and .

The result is .

Calculate the point at x=π .

Replace the variable with in the expression.

Clarify the result.

Simplify each term.

The exact value of is .

Multiply by .

Add and .

The result is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

The common factor should be canceled of .

Cancel the common factor.

Divide by .

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

The exact value of is .

Multiply by .

Sum and .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

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

The exact value of is .

Multiply by .

Multiply by .

Add and .

The result is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Simplify each term.

The common factor should be canceled and .

Factor out of .

The common factors should be canceled.

Factor out of .

Cancel the common factor.

Reformulate the expression.

Divide by .

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

The exact value of is .

Multiply by .

Sum and .

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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