Evaluate sec(pi/6)^2

Problem

sec(π/6)

Solution

1. Identify the trigonometric identity for secant, which is the reciprocal of the cosine function.

sec(π/6)=1/cos(π/6)

2. Determine the value of cos(π/6) using the unit circle or standard trigonometric values.

cos(π/6)=√(,3)/2

3. Substitute this value back into the secant expression and simplify the fraction.

sec(π/6)=1/√(,3)/2

sec(π/6)=2/√(,3)

4. Square the result to find the final value of the expression.

(2/√(,3))2=2/((√(,3))2)

4/3

Final Answer

sec(π/6)=4/3

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