Use a calculator to approximate each value in decimal degrees.
θ = arccos (-0.39876459)

Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arccos, are used to find the angle whose cosine is a given value. For example, if θ = arccos(x), then cos(θ) = x. These functions are essential for solving problems where the angle is unknown and can be found using the ratio of sides in a right triangle.

Cosine Function

The cosine function relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is a fundamental concept in trigonometry, and its values range from -1 to 1. Understanding how to interpret these values is crucial when using inverse functions to find angles.

Calculator Functions

Most scientific calculators have specific functions for calculating inverse trigonometric values. When using a calculator to find arccos(-0.39876459), it is important to ensure that the calculator is set to the correct mode (degrees or radians) to obtain the desired output. Familiarity with these functions enhances accuracy in solving trigonometric problems.