http://www.ck12.org Chapter 5. Trigonometric Functions
5.3 Amplitude of Sinusoidal Functions
Here you will see how changing the radius of a circle affects the graph of the sine function through a vertical stretch.
The amplitude of the sine and cosine functions is the distance between the sinusoidal axis and the maximum or
minimum value of the function. In relation to sound waves, amplitude is a measure of how loud something is.
What is the most common mistake made when graphing the amplitude of a sine wave?
Watch This
Watch the portion of this video discussing amplitude:
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 form a sinusoidal function is:
f(x) =±a·sin(b(x+c))+d
The cosine function can just as easily be substituted and for many problems it will be easier to use a cosine
equation. Since both the sine and cosine waves are identical except for a horizontal shift, it all depends on where
you see the wave starting.
The coefficientais the amplitude (which fortunately also starts with the letter a). When there is no number present,
then the amplitude is 1. The best way to define amplitude is through a picture. Below is the graph of the function
f(x) = 3 ·sinx, which has an amplitude of 3.