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Algebra-2

You will define the terms “period” and “periodic function,” and be able to find the period of a variety of trigonometric functions.

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After completing this tutorial, you will be able to complete the following:

- Explain the concept of period and periodic functions.
- Find the period of sine functions.
- Find the period of cosine functions.
- Find the period of tangent functions.
- Find the period of cotangent functions.

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. |

Course | Algebra-2 |

Type of Tutorial | Guided Discovery |

Key Vocabulary | cosine function, cotangent function, trigonometric functions |