Find the Exact Value sec(-60 degrees )

Problem

sec(−60)

Solution

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

sec(−60)=sec(60)

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

sec(60)=1/cos(60)

3. Substitute the known value for cos(60) from the unit circle, which is 1/2

1/cos(60)=1/(1/2)

4. Simplify the fraction by multiplying by the reciprocal.

1/(1/2)=2

Final Answer

sec(−60)=2

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