Evaluate arcsin(-( square root of 3)/2)

Problem

arcsin(−√(,3)/2)

Solution

1. Identify the range of the inverse sine function, which is [−π/2,π/2]

2. Recall the standard values for the sine function in the first quadrant, specifically that sin(π/3)=√(,3)/2

3. Apply the odd function property of sine, sin(−x)=−sin(x) to find the angle within the required range that yields the given value.

4. Determine that since sin(π/3)=√(,3)/2 then sin(−π/3)=−√(,3)/2

Final Answer

arcsin(−√(,3)/2)=−π/3

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