Find the Exact Value arcsin(sin((5pi)/6))

Problem

arcsin(sin((5*π)/6))

Solution

1. Evaluate the inner trigonometric function sin((5*π)/6) Since (5*π)/6 is in the second quadrant, the sine value is positive.

sin((5*π)/6)=1/2

2. Substitute the value back into the inverse sine function.

arcsin(1/2)

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

θ=π/6

Final Answer

arcsin(sin((5*π)/6))=π/6

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