Evaluate arcsin(sin((5pi)/6))

Problem

arcsin(sin((5*π)/6))

Solution

1. Evaluate the inner function by finding the value of sin((5*π)/6) Since (5*π)/6 is in the second quadrant, the sine value is positive and equal to sin(π−(5*π)/6)=sin(π/6)

sin((5*π)/6)=1/2

2. Identify the range of the inverse sine function, arcsin(x) which is restricted to the interval [−π/2,π/2]

3. Calculate the inverse sine of the result from step 1. We need to find an angle θ in the interval [−π/2,π/2] such that sin(θ)=1/2

arcsin(1/2)=π/6

Final Answer

arcsin(sin((5*π)/6))=π/6

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