You will define the terms period and periodic function, and be able to find the period of a variety of trigonometric functions.
After completing this tutorial, you will be able to complete the following:
The average human heart beats approximately 70 times per minute. Each beat, or cycle, consists of a contraction and a relaxation (also called a systole) controlled by the central nervous system. Each contraction of the heart causes a slight rise in blood pressure; each relaxation causes a small drop in blood pressure. Below is a graph of depicting blood pressure as a function of time.
Mathematicians call functions as the one in the graph above periodic. A periodic function is one that repeats its range over a fixed interval. One complete repetition is called a cycle, and the horizontal length of a cycle is called the period.
Fortunately, these functions have periods that follow a well-defined pattern. This pattern can be proven with the definition of each trigonometric function as a ratio of side lengths in a right triangle. It is summarized in the table below.
|Approximate Time||50 Minutes|
|Pre-requisite Concepts||Learners should have a knowledge of functions, their graphs, and translations; the ability to compute absolute values, take exponents, and reduce fractions; and a basic understanding of trigonometric functions, their definitions, and their graphs.|
|Type of Tutorial||Guided Discovery|
|Key Vocabulary||cosine function, cotangent function, trigonometric functions|