Question

Find the exact value. $\operatorname{arccot}(\sqrt{3})$

   Find the exact value.
$\operatorname{arccot}(\sqrt{3})$

Precalculus

Carl Stitz, Jeff… 3rd Edition

Chapter 10, Problem 32

Instant Answer

Solved by Expert Saurabh Chandra

08/13/2021

Step 1

We can write this as $\operatorname{cot}^{-1}(\sqrt{3})$ and let the value be $t$. Show more…

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Find the exact value. $\operatorname{arccot}(\sqrt{3})$

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Key Concepts

Inverse Trigonometric Functions

Inverse trigonometric functions are functions that give the angle corresponding to a given trigonometric value. They 'undo' the original trigonometric operation, allowing one to find an angle when the value of sine, cosine, tangent, etc., is known.

Arccot Function and Its Principal Value

The arccot function is the inverse of the cotangent function. It returns the angle whose cotangent equals a given number. By convention, the principal value of arccot is chosen within a specific interval to ensure that the function is single-valued, usually between 0 and ?.

Relationship Between Cotangent and Special Angles

The cotangent function relates an angle to the ratio of the adjacent side over the opposite side in a right triangle. For certain standard angles, these ratios are well-known and can be used to determine exact values by referring to special triangles, such as 30°-60°-90° triangles, where the trigonometric ratios are established.

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