In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. tan θ = 0.4169

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 also expressed as tan(θ) = sin(θ)/cos(θ). Understanding this function is crucial for solving problems involving angles and their corresponding ratios.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arctan or tan⁻¹, are used to find the angle when the value of a trigonometric function is known. For example, if tan(θ) = 0.4169, then θ can be found using θ = arctan(0.4169). This concept is essential for determining angles from given ratios.

Radians and Degrees

Radians and degrees are two units for measuring angles. Radians are based on the radius of a circle, where one full rotation (360 degrees) is equivalent to 2π radians. In this problem, the angle θ needs to be expressed in radians, which is important for accurate calculations and interpretations in trigonometry.