Math Homework Help

The phase shift is the horizontal shift away from the standard graph of the trigonometric function.

In y = AsinB(x - C) + D,C is the phase shift.
For cosine function y = AcosB(x - C) + D and tangent function y = AtanB(x - C) + D also C is the phase shift.

If the phase shift is positive, there has been a horizontal shift to the right and if it is negative, there has been a horizontal shift to the left.

In reading off the phase shift, make sure you have the function in the form above.

For example, the phase shift of y = sin(2x - ? /2) is not ?/2. Rewrite the expression for the function in the required form to get
y = sin2(x - ?/4).
Now we see the correct phase shift, is ?/4.

In the graph we can see graph of sin(2x - ? /2) is shifted to ?/4 units to the right.