Simplify tan(arccos(1/2))

Problem

tan(arccos(1/2))

Solution

1. Identify the value of the inner inverse trigonometric function arccos(1/2)

2. Recall the unit circle values where the cosine of an angle θ is equal to 1/2 within the restricted range [0,π]

arccos(1/2)=π/3

3. Substitute this angle back into the original expression to find the tangent.

tan(π/3)

4. Evaluate the tangent of π/3 using the ratio of sine to cosine or known unit circle values.

tan(π/3)=sin(π/3)/cos(π/3)

tan(π/3)=√(,3)/2/1/2

tan(π/3)=√(,3)

Final Answer

tan(arccos(1/2))=√(,3)

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