How do you evaluate ${sin}^{- 1} (\frac{\sqrt{3}}{2})$ $sin^-1(sqrt3/2)$ ?

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How do you evaluate ${sin}^{- 1} (\frac{\sqrt{3}}{2})$ $sin^-1(sqrt3/2)$ ?

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Answer 1 · 2016-11-25T14:45:20

$\frac{π}{3} and \frac{2 π}{3}$ $pi/3 and (2pi)/3$

Explanation:

${sin}^{- 1} (\frac{\sqrt{3}}{2})$ $sin^-1 (sqrt3/2)$ --> $arcsin (\frac{\sqrt{3}}{2})$ $arcsin (sqrt3/2)$
Use trig table of special arcs and trig unit circle -->
$sin x = \frac{\sqrt{3}}{2}$ $sin x = sqrt3/2$ --> there are 2 solutions:
arc $x = \frac{π}{3}$ $x = pi/3$ and arc $x = \frac{2 π}{3}$ $x = (2pi)/3$

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How do you evaluate ${sin}^{- 1} (\frac{\sqrt{3}}{2})$ $sin^-1(sqrt3/2)$ ?

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