Graphs of sine and cosine

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

Types of Problems
There is one type of problem in this exercise:


 * 1) Find the equation of the sinusoid: This problem has the graph of a sine or cosine function. The student is asked to fill in the missing values in the definition of the trigonometric function.Gosac1.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.