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 · 2016-09-16T10:44:28

$- \frac{π}{6}$ $-pi/6$

Explanation:

${tan}^{- 1} (- \frac{\sqrt{3}}{3}) = - \frac{π}{6}$ $tan^-1(-sqrt3/3)= -pi/6$ .Since $tan (- \frac{π}{6}) = - \frac{\sqrt{3}}{3}$ $tan(-pi/6)=-sqrt3/3$ and $- \frac{π}{6} \in (- \frac{π}{2}, \frac{π}{2})$ $-pi/6 in (-pi/2 , pi/2)$ [Ans]

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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?