Find the Exact Value sec(pi/6)

Problem

sec(π/6)

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/6 into the identity.

sec(π/6)=1/cos(π/6)

3. Determine the exact value of cos(π/6) from the unit circle or a special right triangle (30−60−90.

cos(π/6)=√(,3)/2

4. Calculate the reciprocal of the cosine value.

sec(π/6)=1/√(,3)/2

sec(π/6)=2/√(,3)

5. Rationalize the denominator by multiplying the numerator and the denominator by √(,3)

sec(π/6)=(2⋅√(,3))/(√(,3)⋅√(,3))

sec(π/6)=(2√(,3))/3

Final Answer

sec(π/6)=(2√(,3))/3

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