Question

Find the exact value of each expression. $$ \cot ^{-1} 1 $$

   Find the exact value of each expression.
$$
\cot ^{-1} 1
$$

Algebra and Trigonometry

Algebra and Trigonometry

Michael Sullivan 10th Edition

Chapter 8, Problem 38

Instant Answer

Solved by Expert Balaji S

11/24/2020

Step 1

It is defined as $\cot(x) = \frac{1}{\tan(x)}$. Show more…

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Find the exact value of each expression. $$ \cot ^{-1} 1 $$

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Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions are the functions that return the angle corresponding to a given trigonometric ratio. They reverse the roles of the standard trigonometric functions and are essential for determining angle measures when given ratios, especially in problems involving right triangles or periodic behavior.

Arctan Function

The arctan function, also known as the inverse tangent function, provides the angle whose tangent is a given number. It is defined with a limited range, typically from -?/2 to ?/2, to ensure that each value corresponds to a unique angle, thereby making it a proper inverse function.

Unit Circle and Special Angles

The unit circle is a fundamental tool in trigonometry that helps visualize and recall the values of trigonometric functions at various angles. Special angles on the unit circle, such as ?/4 and ?/3, have known tangent values, making them useful in finding the exact values of expressions involving the arctan function.

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