Question

Evaluate without using a calculator. $$\tan ^{-1}\left(\tan 60^{\circ}\right)$$

   Evaluate without using a calculator.
$$\tan ^{-1}\left(\tan 60^{\circ}\right)$$

Trigonometry

Charles P. McKeague,… 7th Edition

Chapter 4, Problem 70

Instant Answer

Solved by Expert Shamshad Waris

11/09/2020

Step 1

Step 1: We know that $\tan ^{-1}\left(\tan x\right)$ is equal to $x$, where $x$ belongs to $-90^{\circ}$ to $90^{\circ}$. Show more…

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Evaluate without using a calculator. $$\tan ^{-1}\left(\tan 60^{\circ}\right)$$

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Key Concepts

Periodicity of the Tangent Function

The tangent function is periodic with a period of 180° (or ? radians), meaning that its values repeat every 180°. This property is important when dealing with inverse functions, as the inverse must account for the repeating nature of the tangent by selecting the appropriate angle within the principal branch.

Principal Value

The principal value is the output of an inverse trigonometric function that falls within a specific, conventional range. For the arctan function, this range is typically between -90° and 90° (or -?/2 and ?/2 radians), ensuring a unique answer even when the original angle might have multiple representations.

Inverse Trigonometric Functions

These functions reverse the process of trigonometric functions, allowing one to find an angle that corresponds to a given trigonometric value. They are defined with restricted ranges so that each input gives a unique output.

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