Find the Exact Value sec(pi/3)

Problem

sec(π/3)

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 π/3 into the identity.

sec(π/3)=1/cos(π/3)

3. Determine the exact value of cos(π/3) using the unit circle or a special right triangle (60.

cos(π/3)=1/2

4. Simplify the expression by calculating the reciprocal of the cosine value.

sec(π/3)=1/(1/2)

sec(π/3)=2

Final Answer

sec(π/3)=2

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