Math Problem Statement

Complete the following statement. The range of the cosine function is​ __________.

Solution

The range of the cosine function is [1,1][-1, 1].

This means that for any input xx, the output of the cosine function will always lie between 1-1 and 11, inclusive.

Would you like more details or have any further questions?

Here are 5 related questions to explore further:

  1. What is the domain of the cosine function?
  2. How is the period of the cosine function defined?
  3. What is the amplitude of the cosine function?
  4. How does the graph of the cosine function look over one period?
  5. How is the cosine function related to the sine function?

Tip: The cosine function repeats its values every 2π2\pi radians, which is known as its period.

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Math Problem Analysis

Mathematical Concepts

Trigonometry
Cosine Function
Range of Functions

Formulas

Range of cosine function: [-1, 1]

Theorems

Cosine Function Properties
Periodic Nature of Trigonometric Functions

Suitable Grade Level

Grades 9-12