Find the Exact Value 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 unit circle values for the sine function, where sin(θ)=y

3. Determine the angle θ within the range [−π/2,π/2] such that sin(θ)=−√(,3)/2

4. Evaluate the angle based on the known value sin(π/3)=√(,3)/2

5. Apply the property sin(−θ)=−sin(θ) to find that sin(−π/3)=−√(,3)/2

Final Answer

arcsin(−√(,3)/2)=−π/3

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