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

Problem

arcsin(cos((7*π)/6))

Solution

1. Evaluate the inner function by finding the value of cos((7*π)/6) Since (7*π)/6 is in the third quadrant, the cosine value is negative.

cos((7*π)/6)=−√(,3)/2

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

arcsin(−√(,3)/2)

3. Determine the angle in the restricted range of the inverse sine function, which is [−π/2,π/2] We need to find θ such that sin(θ)=−√(,3)/2

θ=−π/3

Final Answer

arcsin(cos((7*π)/6))=−π/3

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