Cosine Graph


In this lesson, we will look at graphing the cosine function.

 

 

We will start with the unit circle.
A unit circle is a circle of radius one unit with its centre at the origin.

 

 

For a point (x, y) on the unit circle;

y = cos θ is known as the cosine function.


Using the unit circle, we can plot the values of y against the corresponding values of θ.

The graph of y = cos θ, for 0˚ θ 360˚ obtained is as shown:


 

Properties of the cosine function:

  • The cosine function forms a wave that starts from the point (0,1)
  • cos θ = 0 when θ = 90˚, 270˚.
  • Maximum value of cos θ is 1 when θ = 0˚, 360˚. Minimum value of cos θ is –1 when θ = 180˚. So, the range of values of cos θ is – 1 ≤ cos θ ≤ 1.
  • As the point P moves round the circle in either the clockwise or anticlockwise direction, the cosine curve above repeats itself for every interval of 360˚. Its period is 360˚.


 

 

Example:

The diagram shows a graph of y = cos x for 0˚ ≤ ≤ 360˚, determine the values of p, q and r.
 

Solution:
We know that cos 180˚ = –1. So, p = –1.

We know that for a cosine graph, cos θ = 0 for θ = 90˚ and 270˚.  So, θ = 90˚

We know that for a cosine graph, cos θ = 1 for θ = 0˚ and 360˚. 
So, r = 360˚

 

 

Example:
Sketch the graph of y = 2 cos x for 0˚ ≤ x ≤ 360˚.

Solution:
Set up a table of values for the equation y = 2cos x

x

0

90

180

270

360

cos x

1

0

–1

0

1

2 cos x

2

0

–2

0

2

Plot the points and join with a smooth curve.

 

Also take note that, the graphs of y = sin x and y = cos x, for 0˚ ≤ x ≤ 360˚, intersect at two points: x = 45˚ and x = 225˚.

 

 

 

Videos

Graphing basic sine and cosine functions (in degrees)

 

The Graph of Cosine, y = cos (x)

 

 

 

Custom Search

 

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

 

© Copyright 2005, 2008 - onlinemathlearning.com
Embedded content, if any, are copyrights of their respective owners.

Useful Links:
Trigonometry
 

 

   

 

Custom Search