Find the Value Using the Unit Circle 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. Determine the coordinates on the unit circle for the angle π/3 radians, which corresponds to 60

(x,y)=(cos(π/3),sin(π/3))

3. Evaluate the cosine of π/3 using the unit circle values.

cos(π/3)=1/2

4. Substitute the cosine value into the reciprocal identity to find the secant.

sec(π/3)=1/(1/2)

5. Simplify the fraction by multiplying by the reciprocal.

sec(π/3)=2

Final Answer

sec(π/3)=2

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