In Exercises 55–58, use a calculator to find the value of the acute angle θ to the nearest degree. tan θ = 4.6252

Key Concepts

Tangent Function

The tangent function, denoted as tan(θ), is a fundamental trigonometric function defined as the ratio of the opposite side to the adjacent side in a right triangle. It is crucial for solving problems involving angles and sides in right triangles, and it is periodic with a period of π radians (or 180 degrees). Understanding how to manipulate and interpret the tangent function is essential for finding angles from given ratios.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arctan or tan⁻¹, are used to determine the angle when the value of a trigonometric function is known. For example, if tan(θ) = 4.6252, we can find θ by calculating θ = arctan(4.6252). These functions are vital for solving equations where the angle is the unknown, allowing us to reverse the process of finding the tangent of an angle.

Calculator Usage for Trigonometric Functions

Using a calculator to find trigonometric values involves understanding how to input functions correctly and interpret the results. Most scientific calculators have dedicated buttons for trigonometric functions and their inverses. It is important to ensure that the calculator is set to the correct mode (degrees or radians) based on the context of the problem, as this will affect the output angle.