http://www.ck12.org Chapter 5. Trigonometric Functions
5.5 Frequency and Period of Sinusoidal Functions
tions
Here you will apply your knowledge of horizontal stretching transformations to sine and cosine functions.
The transformation rules about horizontal stretching and shrinking directly apply to sine and cosine graphs. If a sine
graph is horizontally stretched by a factor of^12 that is the same as a horizontal compression by a factor of 2.
How does the equation change when a sine or cosine graph is stretched by a factor of 3?
Watch This
MEDIA
Click image to the left for use the URL below.
URL: http://www.ck12.org/flx/render/embeddedobject/61171http://www.youtube.com/watch?v=qJ-oUV7xL3w James Sousa: Amplitude and Period of Sine and Cosine
Guidance
The general equation for a sinusoidal function is:
f(x) =±a·sin(b(x+c))+d
The±controls the reflection across thex-axis. The coefficientacontrols the amplitude. The constantdcontrols
the vertical shift. Here you will see that the coefficientbcontrols the horizontal stretch.
Horizontal stretch is measured for sinusoidal functions as their periods. This is why this function family is also
called the periodic function family. The period of a sinusoid is the length of a complete cycle. For basic sine and
cosine functions, the period is 2π. This length can be measured in multiple ways. In word problems and in other
tricky circumstances, it may be most useful to measure from peak to peak.