Find the exact value of each real number y if it exists. Do not use a calculator.
y = arccos (―√3/2)

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 y = arccos(x), then cos(y) = x. Understanding these functions is crucial for solving problems that involve finding angles from known trigonometric ratios.

Range of the arccos Function

The arccos function has a specific range of values, which is [0, π] for real numbers. This means that when you calculate arccos for a value, the result will always be an angle between 0 and π radians. Recognizing this range helps in determining the possible values of y when solving equations involving arccos.

Trigonometric Values of Special Angles

Certain angles have known trigonometric values, which are often derived from the unit circle. For instance, cos(5π/6) = -√3/2. Familiarity with these special angles allows for quick identification of exact values when solving trigonometric equations, such as the one presented in the question.