How do you evaluate $arctan (\frac{\sqrt{3}}{3})$ $arctan(sqrt3/3)$ without a calculator?

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How do you evaluate $arctan (\frac{\sqrt{3}}{3})$ $arctan(sqrt3/3)$ without a calculator?

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Answer 1 · 2017-12-02T13:14:33

The answer is $\frac{π}{6}$ $pi/6$

Explanation:

We can do that easily by rationalizing the numerator
we get ${tan}^{- 1} [\frac{\sqrt{3}}{3}] = {tan}^{- 1} [\frac{\sqrt{3} . \sqrt{3}}{3 . \sqrt{3}}] = {tan}^{- 1} [\frac{3}{3 . \sqrt{3}}] = arctan (\frac{1}{\sqrt{3}}) = \frac{π}{6}$ $tan^-1[(sqrt3)/3]=tan^-1[(sqrt3.sqrt3)/(3.sqrt3)]=tan^-1[3/(3.sqrt3)]=arctan(1/(sqrt3))=pi/6$

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How do you evaluate $arctan (\frac{\sqrt{3}}{3})$ $arctan(sqrt3/3)$ without a calculator?

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