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ZingPath: Problem Solving with Trigonometric Functions

Finding the Period of a Trigonometric Function

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Problem Solving with Trigonometric Functions

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Lesson Focus

Finding the Period of a Trigonometric Function

Algebra-2

Learning Made Easy

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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Now You Know

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.

Everything You'll Have Covered

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.

Tutorial Details

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