Amplitude of trigonometric functions

The  exercise appears under the Trigonometry Math Mission. This exercise develops the idea of the amplitude of a trigonometric function.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the amplitude from the graph: This problem provides a graph of a trigonometric function. The student is asked to use the graph and find the value of the amplitude.Aotf1.png
 * 2) Find the amplitude from the function: This problem provides the formula of a trigonometric function. The student is asked to use the function and find the value of the amplitude.Aotf2.png

Strategies
Knowledge of the trigonometric ratios and a general idea of the trigonometric graphs are encouraged to ensure success on this exercise.
 * 1) Amplitude only makes sense on the sine and cosine graphs.
 * 2) The amplitude is half the distance between the maximum and minimum values of the graph.
 * 3) The amplitude is the distance from the midline to either the top or bottom of the graph.
 * 4) In a formula form, the amplitude is the coefficient in front of the trig function. This is a vertical stretch or compression factor.

Real-life Applications

 * 1) Trigonometric graphs have applications in wave motion, such as light and sound.
 * 2) Sinusoids can be used to represent periodic motion, such as temperatures and tides.