Simplify 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 property of the inverse sine function for negative values, which states arcsin(−x)=−arcsin(x)

3. Apply the property to rewrite the expression as −arcsin(√(,3)/2)

4. Determine the angle θ in the interval [0,π/2] such that sin(θ)=√(,3)/2

5. Evaluate the value using known trigonometric values, where sin(π/3)=√(,3)/2

6. Combine the results to find the final value.

Final Answer

arcsin(−√(,3)/2)=−π/3

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