Find the Exact Value sec(60)

Problem

sec(60^∘)

Solution

1. Identify the relationship between the secant function and the cosine function using the reciprocal identity.

sec(θ)=1/cos(θ)

2. Substitute the given angle of 60^∘ into the identity.

sec(60^∘)=1/cos(60^∘)

3. Determine the exact value of cos(60^∘) using the unit circle or a special right triangle (30^∘−60^∘−90^∘.

cos(60^∘)=1/2

4. Simplify the expression by dividing 1 by the fraction.

sec(60^∘)=1/(1/2)

sec(60^∘)=2

Final Answer

sec(60^∘)=2

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