# Graph f(t) equals three sin(four t)

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 common factor should be canceled of and .

Factor out of .

The common factors should be canceled.

Factor out of .

Cancel the common factor.

Reformulate the expression.

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.

First, multiply by .

The exact value of is .

Multiply by .

The result is .

Calculate the point at x=π .

Replace the variable with in the expression.

Clarify the result.

The common factor should be canceled.

Factor out of .

Cancel the common factor.

Should be rewritten the expression.

The exact value of is .

Multiply by .

The result is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

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

The exact value of is .

Multiply by .

The final answer is .

Find the point at .

Replace the variable with in the expression.

Simplify the result.

Cancel the common factor of .

Factor out of .

Cancel the common factor.

Rewrite the expression.

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 .

Multiply by .

The result is .

Calculate the point at .

Replace the variable with in the expression.

Simplify the result.

The common factor should be canceled.

Factor out 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 .

Multiply 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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