1. Graphs of Cosine
Section 4-5

2. Objectives I can determine all key values for 6 trig functions
I can graph cosine functions
I can determine amplitude, period, and phase shifts of cosine functions

3. Graph of the Cosine Function
To sketch the graph of y = cos x first locate the key points. These are the maximum points, the minimum points, and the intercepts. 1 -1
cos x x
Then, connect the points on the graph with a smooth curve that extends in both directions beyond the five points. A single cycle is called a period. y x
y = cos x
Cosine Function

4. Properties of Sine and Cosine Functions
The graphs of y = sin x and y = cos x have similar properties:
1. The domain is the set of real numbers. (-∞, ∞)
2. The range is the set of y values such that
3. The maximum value is 1 and the minimum value is –1.
4. The graph is a smooth curve.
5. Each function cycles through all the values of the range over an x-interval of
6. The cycle repeats itself indefinitely in both directions of the x-axis.
Properties of Sine and Cosine Functions

5. Graphing Trig Functions
Find the period of the function
We will use the following to graph:
“x” represents radians
“” represents degrees
Example: sin x versus sin 
Determine the key points (Make data table)
Intercepts
Maximum points
Minimum points

6. y = cos x
Start HIGH, middle, low, middle, high

7. Example: Sketch the graph of y = 3 cos x on the interval [–, 4].
Partition the interval [0, 2] into four equal parts. Find the five key points; graph one cycle; then repeat the cycle over the interval.
max
x-int
min 3 -3
y = 3 cos x 2  x y x
(0, 3)
( , 3)
( , 0)
( , 0)
( , –3)
Example: y = 3 cos x

8. θ 90
180
270
360
Cos 1 -1
2 Cos 2 -2 Rx
45 degrees
Left
-45 45
135
225
315 90
180
270
360
-90
-180
-270
-360

9. White Board

10. White Board

11. Homework
Trig Value Table
WS 9-2