Find the Exact Value arcsin(sin((7pi)/6))

Problem

arcsin(sin((7*π)/6))

Solution

1. Evaluate the inner trigonometric function sin((7*π)/6) Since (7*π)/6 is in the third quadrant, the sine value is negative.

sin((7*π)/6)=−1/2

2. Identify the range of the inverse sine function. The output of arcsin(x) must fall within the interval [−π/2,π/2]

3. Find the angle θ in the interval [−π/2,π/2] such that sin(θ)=−1/2

arcsin(−1/2)=−π/6

Final Answer

arcsin(sin((7*π)/6))=−π/6

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