How do you find the value of $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ ?

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How do you find the value of $arcsin (- \frac{\sqrt{3}}{2})$ $arcsin(-sqrt3/2)$ ?

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Answer 1 · 2016-12-30T13:21:41

$\frac{4 π}{3}, \frac{5 π}{3}$ $(4pi)/3, (5pi)/3$

Explanation:

Use trig table and unit circle:
$sin x = - \frac{\sqrt{3}}{2}$ $sin x = - sqrt3/2$ -->
arc $x = - \frac{π}{3}$ $x = - (pi)/3$ and arc $x = - \frac{2 π}{3}$ $x = - (2pi)/3$
Co-terminal arc of $(- \frac{π}{3}) - \to \frac{4 π}{3}$ $(-pi/3) --> (4pi)/3$
Co-terminal of $\frac{- 2 π}{3} - \to \frac{5 π}{3}$ $(-2pi)/3 --> (5pi)/3$
Answers for $(0, 2 π)$ $(0, 2pi)$
$\frac{4 π}{3}, \frac{5 π}{3}$ $(4pi)/3, (5pi)/3$

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