Final answer:
The exact value of sec 11π/3 is found by simplifying the angle to 2π/3, which is in the second quadrant where cosine is negative. The cosine at 2π/3 is -1/2, hence the secant is -2.
Step-by-step explanation:
To find the exact value of the trigonometric function sec 11π/3, we need to first understand the secant function and how it relates to the unit circle. The secant function, sec(θ), is the reciprocal of the cosine function, which means sec(θ) = 1/cos(θ). To simplify the angle 11π/3, we can find an equivalent angle by subtracting multiples of 2π (360° in degrees) until the resulting angle is within the interval [0, 2π].
11π/3 is the same as (9π/3) + (2π/3), which is equivalent to 3π + (2π/3). Since 3π/3 is a full circle (2π), 11π/3 is equivalent to 2π/3 after subtracting 3π (or a full circle). The angle 2π/3 is located in the second quadrant of the unit circle, where the cosine is negative. We can now find the value of cosine at 2π/3 which is -1/2, hence the secant at that angle will be -2 (since sec(θ) = 1/cos(θ) and sec(2π/3) = 1/(-1/2)).
The exact value of sec 11π/3 is -2.