In Exercises 59–62, use a calculator to find the value of the acute angle θ in radians, rounded to three decimal places. cos θ = 0.4112

Key Concepts

Cosine Function

The cosine function is a fundamental trigonometric function defined as the ratio of the adjacent side to the hypotenuse in a right triangle. It is denoted as cos(θ) and is crucial for determining the angle when the cosine value is known. In this context, cos(θ) = 0.4112 indicates the relationship between the angle θ and the lengths of the sides of a right triangle.

Inverse Trigonometric Functions

Inverse trigonometric functions, such as arccosine (cos⁻¹), are used to find angles when the value of a trigonometric function is known. For example, to find θ when cos(θ) = 0.4112, one would use θ = cos⁻¹(0.4112). This process is essential for solving for angles in trigonometric equations.

Radians

Radians are a unit of angular measure used in mathematics, particularly in trigonometry. One radian is the angle formed when the arc length is equal to the radius of the circle. In this problem, the angle θ needs to be expressed in radians, which is important for consistency in calculations and when using calculators that may default to radians.