Simplify sec(pi/6)

Problem

sec(π/6)

Solution

1. Identify the definition of the secant function in terms of the cosine function.

sec(θ)=1/cos(θ)

2. Substitute the given angle into the definition.

sec(π/6)=1/cos(π/6)

3. Evaluate the cosine of π/6 using the unit circle or special right triangles.

cos(π/6)=√(,3)/2

4. Simplify the complex fraction by multiplying by the reciprocal.

1/√(,3)/2=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

sec(π/6)=(2√(,3))/3

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