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Chapter 5: Problem 9

Evaluate the expression without using a calculator. \(\arctan \frac{\sqrt{3}}{3}\)

Short Answer

Expert verified
The evaluated result of the expression is \(\frac{\pi}{6}\).

Step by step solution

01

Identifying equivalent tangent values

Firstly, find the angle from the unit circle whose tangent value is \(\frac{\sqrt{3}}{3}\). This can be identified as \(\frac{\pi}{6}\).
02

Use the arctangent function

The \(\arctan\) function returns the angle whose tangent is given by the input. So, using this property, we get \(\arctan (\tan(\frac{\pi}{6}))\).
03

Simplification

The arctan and tan functions are inverses of one another, thus they cancel each other out. Hence, we get \(\arctan (\tan(\frac{\pi}{6})) = \frac{\pi}{6}\).

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