Find the Exact Value sec(-pi/3)

Problem

sec(−π/3)

Solution

1. Use the even-odd identity for the secant function, which states that sec(−θ)=sec(θ)

sec(−π/3)=sec(π/3)

2. Apply the reciprocal identity to express secant in terms of cosine.

sec(π/3)=1/cos(π/3)

3. Evaluate the cosine of the reference angle π/3 (or 60 using the unit circle or special triangles.

cos(π/3)=1/2

4. Simplify the fraction by taking the reciprocal of the cosine value.

1/(1/2)=2

Final Answer

sec(−π/3)=2

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