Find the Exact Value arcsin(sin((11pi)/6))

Problem

arcsin(sin((11*π)/6))

Solution

1. Evaluate the inner trigonometric function sin((11*π)/6)

2. Identify the reference angle for (11*π)/6 which is π/6 Since (11*π)/6 is in the fourth quadrant, the sine value is negative.

sin((11*π)/6)=−1/2

3. Substitute this value back into the inverse sine function.

arcsin(−1/2)

4. Determine the angle θ such that sin(θ)=−1/2 within the restricted range of the arcsine function, which is [−π/2,π/2]

5. Conclude that the angle in this range is −π/6

Final Answer

arcsin(sin((11*π)/6))=−π/6

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