Title: 13.5 – The Cosine Function
113.5 The Cosine Function
2The Cosine Function
Find the x-coordinate of each point on the unit
circle. 1. A 2. B 3. C 4. D
3The Cosine Function
1. x-coordinate of point A 1 2. x-coordinate of
point B 0 3. x-coordinate of point C
1 4. x-coordinate of point D 0
Solutions
4The Cosine Function
The
5Highlights of the Cosine Function
- The cosine function, matches
the measure of an angle in standard position with
the x-coordinate of a point on the unit circle.
- Within one cycle of the function the graph will
zero by touching the x axis two times (
) reach a minimum value of -1 at and
a maximum value of 1 at 0 and .
6Differences and Similarities between the sine and
cosine functions
7Graphing the Cosine Function
Sketch the graph of
- Steps
- Determine the amplitude. In this case a 2.
- Determine the period using the formula .
This will be the outer boundary of your graph. - Period
- 3. Use five points equally spaced through one
cycle to sketch a cosine curve. The fivepoint
pattern is - maxzerominzero-max.
- Plot the points.
8
8Graphing the Cosine Function
Sketch the graph of
Steps 4. Make a smooth curve through the points
to complete your graph.
8
9The Cosine Function
Use the graph shown below.
a. Find the domain, period range, and amplitude
of this function.
The domain of the function is all real numbers.
10The Cosine Function
(continued)
b. Examine the cycle of the cosine function in
the interval from 0 to 2 . Where in
the cycle does the maximum value occur? Where
does the minimum occur? Where do the zeros occur?
11The Cosine Function
Sketch the graph of y 2 cos
in the interval from 0 to 4.
12The Cosine Function
Suppose 8-in. waves occur every 6 s. Write an
equation that models the height of a water
molecule as it moves from crest to crest.
13The Cosine Function
2x 3
In the function y 2 cos , for which
values of x is the function equal to 1?
The graph show two solutions in the interval.
They are x 3.14 and 6.28.