# Find the exact value of sin <mrow class="MJX-TeXAtom-ORD"> &#x2212;<!-- − -->

Find the exact value of ${\mathrm{sin}}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$ and the like.
a. ${\mathrm{sin}}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$
b. ${\mathrm{cot}}^{-1}\left(-1\right)$
c. ${\mathrm{sec}}^{-1}\left(\frac{2}{\sqrt{3}}\right)$
d. ${\mathrm{cos}}^{-1}\left(-\frac{\sqrt{2}}{2}\right)$
e. ${\mathrm{tan}}^{-1}\left(-\sqrt{3}\right)$
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Erick Blake
There are a few values of sin or cos that you should know, e.g. $\mathrm{sin}\left(\pi /3\right)=\sqrt{3}/2$. Using the fact that sin is an odd function, $\mathrm{sin}\left(-\pi /3\right)=-\sqrt{3}/2$. So ${\mathrm{sin}}^{-1}\left(-\sqrt{3}/2\right)=-\pi /3$