Find the Exact Value sec(-(11pi)/6)

Problem

sec(−(11*π)/6)

Solution

1. Apply the even-odd property of the secant function, which states sec(−θ)=sec(θ)

sec(−(11*π)/6)=sec((11*π)/6)

2. Find the coterminal angle or identify the position on the unit circle. The angle (11*π)/6 is in the fourth quadrant.

(11*π)/6=2*π−π/6

3. Determine the reference angle for (11*π)/6 which is π/6 In the fourth quadrant, secant is positive.

sec((11*π)/6)=sec(π/6)

4. Use the reciprocal identity sec(θ)=1/cos(θ) to evaluate the expression.

sec(π/6)=1/cos(π/6)

5. Substitute the known value cos(π/6)=√(,3)/2

1/√(,3)/2=2/√(,3)

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

(2√(,3))/3

Final Answer

sec(−(11*π)/6)=(2√(,3))/3

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