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

Graph f(t)=3sin(4t)
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 of .
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.
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:
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:
Select a few points to graph.
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 .
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 .