wku/~tom.richmond/Cosine.html

Animation of the Sine curve: http://www.wku.edu/~tom.richmond/Sine.html Animation of the Cosine curve: http://www.wku.edu/~tom.richmond/Cosine.html

Phase Shift

The only transformation of the function is a phase shift. The amount of the shift can be calculated by: In this case, c = π & k = 1 In this case,

Midline: A new horizontal axis that results from an upward or downward shift. For the graph of Since h = -5, the graph will shift down 5 units. The midline of the graph is y = -5. The amplitude is 2, so the graph will stretch vertically.

The midline is the equation: Graph it. y = -6 Use dashed lines to mark max & mins The amplitude is: 4 The phase shift is: k = ½ The period is: This is the graph before the horizontal (phase) shift C is positive; shift to left. - 6

Example 4 12.4

Use the phase shift to solve for c Use the period to solve for K BEFORE you can find c (replace k with 2 & criss-cross) Solve for k (criss-cross) Divide both sides by π

Then graph the ordered pairs: First, calculate the cos x, then add it to x for your y values to graph. At this point, freehand the curve along y = x 1

HW: Page 383

wku/~tom.richmond/Cosine.html