Midline of trigonometric functions

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

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


 * 1) Find the equation of the midline from the graph: This problem provides a graph of a trigonometric function. The student is asked to use the graph and find the equation of the midline.Motf1.png
 * 2) Find the equation of the midline from the function: This problem provides the formula of a trigonometric function. The student is asked to use the function and find the equation of the midline.Motf2.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 midline is y=k where k is the average of the minimum and maximum values of the function.
 * 2) In a formula form, the midline is found by analyzing the vertical shift. The equation is y=k where k is the number added to the trigonometric function to perform the vertical shift.

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.