Difference between revisions of "008A Sample Final A, Question 19"

Latest revision as of 23:04, 25 May 2015

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:
$\arcsin -{\frac {\sqrt {3}}{2}}=-{\frac {\pi }{3}}$

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 |<math>\arcsin -\frac{\sqrt{3}}{2} = - \frac{\pi}{3}</math>