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Chapter 4: Problem 9

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

Short Answer

Expert verified
The evaluation of the expression \(\arctan \frac{\sqrt{3}}{3}\) gives the result \(\frac{蟺}{6}\) radians.

Step by step solution

01

Recognize common values

Recognize that \(\frac{\sqrt{3}}{3}\) is actually the same as \(\frac{1}{\sqrt{3}}\), which corresponds to \(\tan\left(\frac{蟺}{6}\right)\) or \(\tan(30掳)\) in unit circle.
02

Apply the arctangent

We know that the arctangent function, \(\arctan(x)\), is the angle whose tangent is \(x\). Therefore, if \(\tan(30掳) = \frac{1}{\sqrt{3}}\), then \(\arctan\left(\frac{1}{\sqrt{3}}\right) = 30掳\). But since the question might want the result in radians, we should convert it: \(30掳 = \frac{蟺}{6}\) radians.

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