Graphs of trigonometric functions

The Graphs of trigonometric functions exercise appears under the Trigonometry Math Mission and Differential calculus Math Mission. This exercise connects the graph of a trigonometric function with its 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 user is expected to fully write the equation of the trigonometric function in the space provided.

   

   Write a formula for the trigonometric function

2. Create the graph of the trigonometric function: This problem has the formula for a sinusoid. The user is expected to move some points on the graphing manipulative to create the graph of the trigonometric function.

   

   Create the graph of the trigonometric function

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 ${A\text{trig}(B(x-C))+D}$.
   1. A is the amplitude of the trig function.
   2. B is the horizontal scale factor, and the period is ${\frac{2\pi}{B}}$.
   3. C is the horizontal shift.
   4. D is the vertical shift.
2. 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.
3. Trigonometry has many applications in astronomy, music, analysis of financial markets, and many more professions.