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 Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle -{\frac {\sqrt {3}}{2}}} ?	Answer:
1) The range of arcsin is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle [-{\frac {\pi }{2}},{\frac {\pi }{2}}]} .
2) $\sin(-{\frac {\pi }{3}})=-{\frac {\sqrt {3}}{2}}$.

Solution:

Step 1:
Since the range of $\arcsin$ is Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle [-{\frac {\pi }{2}},{\frac {\pi }{2}}]} , the answer must be in that range.

Final Answer:
Since Sine only equals Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\frac {\sqrt {3}}{2}}} for one value in that range, $\arcsin -{\frac {\sqrt {3}}{2}}=-{\frac {\pi }{3}}$

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