Find the Exact Value arccos(cos(-pi/6))

Problem

arccos(cos(−π/6))

Solution

1. Evaluate the inner cosine function using the even-odd identity cos(−θ)=cos(θ)

cos(−π/6)=cos(π/6)

2. Determine the exact value of cos(π/6) from the unit circle.

cos(π/6)=√(,3)/2

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

arccos(√(,3)/2)

4. Identify the angle θ in the restricted range of arccosine, [0,π] such that cos(θ)=√(,3)/2

θ=π/6

Final Answer

arccos(cos(−π/6))=π/6

Want more problems? Check here!