http://www.ck12.org Chapter 5. Trigonometric Functions
5.2 The Sinusoidal Function Family
Here you will see how the graphs of sine and cosine come from the unit circle.
The cosine function is thexcoordinates of the unit circle and the sine function is theycoordinates. Since the unit
circle has radius one and is centered at the origin, both sine and cosine oscillate between positive and negative one.
What happens when the circle is not centered at the origin and does not have a radius of 1?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61165http://www.youtube.com/watch?v=nXx2PsgMjYA James Sousa: Graphing the Sine and Cosine Functions
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61167http://www.youtube.com/watch?v=QNQAkUUHNxo James Sousa: Animation: Graphing the Sine Function Using
the Unit Circle
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61169http://www.youtube.com/watch?v=tcjZOGaeoeo James Sousa: Animation: Graphing the Cosine Function Using
the Unit Circle
Guidance
Consider a Ferris wheel that spins evenly with a radius of 1 unit. It starts at (1, 0) or an angle of 0 radians and spins
counterclockwise at a rate of one cycle per 2πminutes (so you can use time is equal to radians).