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

Problem

sec((11*π)/6)

Solution

1. Identify the reference angle by determining how far the angle is from the nearest multiple of π on the x-axis.

(11*π)/6=2*π−π/6

Reference Angle=π/6

2. Determine the quadrant of the angle. Since (11*π)/6 is between (3*π)/2 and 2*π it lies in Quadrant IV.

3. Determine the sign of the secant function in Quadrant IV. Since sec(θ)=1/cos(θ) and cosine is positive in Quadrant IV, secant is also positive.

sec((11*π)/6)=sec(π/6)

4. Apply the reciprocal identity for secant.

sec(π/6)=1/cos(π/6)

5. Substitute the known value for cos(π/6)

cos(π/6)=√(,3)/2

6. Simplify the fraction by multiplying by the reciprocal.

sec((11*π)/6)=2/√(,3)

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

2/√(,3)⋅√(,3)/√(,3)=(2√(,3))/3

Final Answer

sec((11*π)/6)=(2√(,3))/3

Want more problems? Check here!