Period of trigonometric functions

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

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


 * 1) Find the period from the graph: This problem provides a graph of a trigonometric function. The student is asked to use the graph to find the value of the period as an exact expression.Potf1.png
 * 2) Find the period from the function: This problem provides the formula of a trigonometric function. The student is asked to use the function and find the exact value of the period.Potf2.png

Strategies
Knowledge of the trigonometric ratios and a general idea of the trigonometric graphs are encouraged to ensure success on this exercise.
 * 1) The period of a graph is how long it takes to complete one cycle, or one over the frequency.
 * 2) The points that are labeled on the given graph can be used to find some fraction of the period, then multiplied to find the full period.
 * 3) In a formula form, the period is $$2\pi $$ divided by the coefficient of x in the function. The coefficient of x performs a horizontal compression or stretch which explains why the period is affected.

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.