Graphs of trigonometric functions

The  exercise appears under the Trigonometry Math Mission. This exercise connects the graph of a trigonometric function with it's functional form by both creating the graph and finding the functional form.

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


 * 1) Write a formula for the trigonometric function: This problem has a graph with a few labeled points. The student is expected to fully write the equation of the trigonometric function in the space provided.Gotf1.png
 * 2) Create the graph of the trigonometric function: This problem has the formula for a sinusoid. The student is expected to move some points on the graphing manipulative to create the graph of the trigonometric function.Gotf2.png

Strategies
Knowledge of the parent functions for sine and cosine and the functional transformations are encouraged to ensure success on this exercise.
 * 1) The general form of a trig function is $$Atrig(B(x-C))+D $$.
 * 2) A is the amplitude of the trig function.
 * 3) B is the horizontal scale factor, and the period is $$\frac{2\pi}{B}$$.
 * 4) C is the horizontal shift
 * 5) D is the vertical shift
 * 6) The problems in this exercise do not seem to have horizontal or vertical shifts.

Real-life Applications

 * 1) Sinusoids are used to model periodic behavior, such as the number of hours of daylight, or temperature cycles over a day, or a year.
 * 2) Light and sound travel in waves that are shaped like sine and cosine curves.