Determine whether the positive or negative square root should be selected.
cos 58° = ±√ (1 + cos 116°)/2]

Key Concepts

Cosine Function

The cosine function is a fundamental trigonometric function that relates the angle of a right triangle to the ratio of the length of the adjacent side to the hypotenuse. It is periodic and oscillates between -1 and 1. Understanding the properties of the cosine function is essential for solving trigonometric equations and determining the values of angles.

Trigonometric Identities

Trigonometric identities are equations that involve trigonometric functions and are true for all values of the variables involved. One important identity is the cosine double angle formula, which states that cos(2θ) = 2cos²(θ) - 1. This identity can be used to simplify expressions and solve equations involving cosine, such as the one presented in the question.

Square Roots and Their Sign

When dealing with square roots in trigonometric equations, it is crucial to consider both the positive and negative roots. The choice between the positive or negative root often depends on the context of the problem, such as the quadrant in which the angle lies. In this case, understanding the range of the cosine function and the specific angle values will guide the correct selection of the square root.