6.5 Notes

Graphing trigonometric functions transformationally:

changes to C and D

Phase Shift and Vertical Shift

To modify the phase shift of a graph of a trigonometric function, modify the value of C in the trigonometric equation. To modify the vertical shift of a graph of a trigonometric function, modify the value of D in the trigonometric equation.

trigy A B C D

Phase Shift and Vertical Shift Like those of the prior lessons and

homework, the instructions for tonight’s homework say to graph the pair of functions on the same graph using conventional graphing techniques.

The first of the pair is the parent function, but graphing the parent is NOT required.

This is the last lesson in which the examples will include the parent graph.

Phase Shift and Vertical Shift Prior to now, you have been encouraged to

practice labeling the horizontal axis (typically x or θ) in radians, as well as, degrees.

Now that we’re graphing trigonometric functions with phase shifts, the horizontal axis should be labeled in the system (degrees or radians) corresponding to that of the value being added to the angle variable.

cot , cot 90y y

csc , cscy x y x

3 32 0 2

2 2 2 2

sin , sin 1y y

3 50 2 3

2 2 2 2

3 50 2 3

2 2 2 2

cos , cos 45 2y x y x