8A F11 Q19

Question: Compute $\arcsin -{\frac {\sqrt {3}}{2}}$. Provide your answer in radians.

Foundations
1) What is the range of $\arcsin$?
2) Sine of what angle in the range of $\arcsin$ yields $-{\frac {\sqrt {3}}{2}}$?	Answer:
1) The range of arcsin is $[-{\frac {\pi }{2}},{\frac {\pi }{2}}]$.
2) $\sin(-{\frac {\pi }{3}})=-{\frac {\sqrt {3}}{2}}$.

Solution:

Step 1:
Since the range of $\arcsin$ is $[-{\frac {\pi }{2}},{\frac {\pi }{2}}]$, the answer must be in that range.

Final Answer:
Since Sine only equals ${\frac {\sqrt {3}}{2}}$ for one value in that range, $\arcsin -{\frac {\sqrt {3}}{2}}=-{\frac {\pi }{3}}$

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