Problems 64-67 are based on material learned earlier in the...

Problems 64-67 are based on material learned earlier in the course. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for the final exam.
Find the exact value of $\cos ^{-1}\left(\frac{1}{\sqrt{2}}\right)$.

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Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions, such as cosine inverse, are the functions that return the angle corresponding to a given trigonometric value. They are defined with restricted domains to make them one-to-one, ensuring that each input corresponds to a unique output. These functions are essential for solving equations where the unknown is an angle rather than a trigonometric ratio.

Principal Value Branch

The principal value branch of an inverse trigonometric function refers to the specific range of angle values chosen so that the function is uniquely defined. For the cosine inverse function, the principal values are typically taken from 0 to ?. Understanding this concept is crucial when determining the appropriate angle that corresponds to a given trigonometric value.

Special Angles in Trigonometry

Special angles in trigonometry refer to angles for which the trigonometric functions have known exact values. These angles are often found by studying the unit circle and include values such as 0, ?/6, ?/4, ?/3, and ?/2 among others. Knowledge of these angles and their properties simplifies the evaluation of trigonometric expressions and is a foundational aspect of trigonometry.

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