How do you find the exact value of arctan of -1/sqrt[3]?

Question

How do you use the properties of inverse trigonometric functions to evaluate $tan (arcsin (0.31))$ $tan(arcsin (0.31))$ ?
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How do you find the exact value of $cos ({tan}^{- 1} \sqrt{3})$ $\cos(tan^{-1}sqrt{3})$ ?
How do you evaluate ${sec}^{- 1} \sqrt{2}$ $\sec^{-1} \sqrt{2}$ ?
How do you find $cos ({cot}^{- 1} \sqrt{3})$ $cos( cot^{-1} sqrt{3} )$ without a calculator?
How do you rewrite ${sec}^{2} ({tan}^{- 1} x)$ $sec^2 (tan^{-1} x)$ in terms of x?
How do you use the inverse trigonometric properties to rewrite expressions in terms of x?
How do you calculate ${sin}^{- 1} (0.1)$ $sin^-1(0.1)$ ?
How do you solve the inverse trig function ${cos}^{- 1} (- \frac{\sqrt{2}}{2})$ $cos^-1 (-sqrt2/2)$ ?
How do you solve the inverse trig function $sin ({sin}^{- 1} (\frac{1}{3}))$ $sin(sin^-1 (1/3))$ ?

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Answer 1 · 2015-08-19T04:10:35

Find $arctan (- \frac{1}{\sqrt{3}})$ $arctan (-1/sqrt3)$

Ans: $\frac{5 π}{6}$ $(5pi)/6$

Trig table gives -->
$tan x = - \frac{1}{\sqrt{3}} = - \frac{\sqrt{3}}{3}$ $tan x = - 1/sqrt3 = - sqrt3/3$ --> arc $x = \frac{5 π}{6}$ $x = (5pi)/6$