# Graph g(x) equals four sin(pix) minus three

Graph g(x)=4sin(pix)-3
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.
is approximately which is positive so remove the absolute value
The common factor should be canceled of .
Cancel the common factor.
First, divide by .
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, 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.
Clarify each term.
First, multiply by .
The exact value of is .
Multiply by .
Subtract from .
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 .
Subtract from .
The result is .
Calculate the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Multiply by .
Use the reference angle by calculating the angle with equivalent triginometric values in the Initially quadrant.
The exact value of is .
Multiply by .
Subtract from .
The final answer is .
Find the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Combine and .
Put to the left of .
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 .
Subtract from .
The final answer is .
Calculate the point at .
Replace the variable with in the expression.
Simplify the result.
Simplify each term.
Put to the left of .
Subtract full rotations of until the angle is greater than or equal to and less than .
The exact value of is .
Multiply by .
Subtract from .
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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