T5.1b To Graph the Cosine Curve Do not say the answers out loud!!! 11-17-14 T5.1b To Graph the Cosine Curve Do not say the answers out loud!!! 1. Put up your dukes. 2. Living off the land. 3. Pleading the fifth. 4. Backhand slice.

OPENER: Together, as a group, determine the equation of this graph: y = -4 sin(x)

Active Learning Assignment? “0” Max “0” Min “0”

* LESSON: Standard form for Cosine Function: y = a*cos b * (x – h) + k Let’s look at the cosine curve on a Gizmo: *

Cosine: More Patterns, Patterns, Patterns! The HORIZONTAL pattern has: beginning, ¼, ½, ¾, and end marks. (same as sine). One normal period, horizontally, is: 0, π/2, π, 3π/2, 2π. (same as sine, and will also change.) Graph y = cos(x) beginning ¼ ½ ¾ end

* The positive VERTICAL pattern has: max, “0”, min, “0”, max (“0” is the middle.) The normal max is 1 and the normal min is -1 (different from sine) * Graph y = cos(x) max 1 “0” min -1 Max “0” Min “0” Max Always write both the x and y coordinates!!!

Graph y = cos(x) Max “0” Min “0” Max

What happens when we multiply the sine function by a number? y = cos(x) vs. y = 2cos(x) This change is called the amplitude. The equation is y = a cos(x)

Graph y = 5cos(x) Max “0” Min “0” Max

Graph y = –1/5 cos(x) Min “0” Max “0” Min

Active Learning Assignment: Graph I: 1, 4, 5, 8 Writing: Compare and contrast the sine and cosine curves Find at least two ways that they are alike, and two ways that they are different.