How do you find ${cot}^{- 1} (- \frac{1}{\sqrt{3}})$ $cot^-1 (-1/sqrt3)$ without using a calculator?

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How do you find ${cot}^{- 1} (- \frac{1}{\sqrt{3}})$ $cot^-1 (-1/sqrt3)$ without using a calculator?

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Answer 1 · 2015-07-08T08:31:29

150, 330 degrees

Explanation:

Let the given expression be equal to y, so that cot y= $- \frac{1}{\sqrt{3}}$ $-1/sqrt3$ .
$\frac{1}{\sqrt{3}}$ $1/sqrt3$ is the value of cot for 30 degrees, as can be seen from the unit circle.

Since cot would be negative in IInd and IVth quadrant, coty would be $- \frac{1}{\sqrt{3}}$ $-1/sqrt3$ for y= 180-30= 150 and y= 360-30= 330 degrees

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How do you find ${cot}^{- 1} (- \frac{1}{\sqrt{3}})$ $cot^-1 (-1/sqrt3)$ without using a calculator?

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How do you find cot−1(−1√3)cot^-1 (-1/sqrt3) without using a calculator?

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How do you find ${cot}^{- 1} (- \frac{1}{\sqrt{3}})$ $cot^-1 (-1/sqrt3)$ without using a calculator?