Question

Find the exact value of sec(-4π/3

Answer 1

Find the exact value of sec(-4π/3). Note that one full rotation, clockwise, would be -2pi. We have to determine the Quadrant in which this angle -4pi/3 lies. Think of this as 4(-pi/3), or 4(-60 degrees). Starting at the positive x-axis and rotating clockwise, we reach -60, -120, -180 and -240 degrees. This is in Q III. The ray representing -240 has adj side = -1 and opp side = to sqrt(3).

Using the Pyth. Theorem to find the length of the hypo, we get hyp = 2.

Thus, the secant of this angle in QIII is hyp / adj, or 2 / sqrt(3) (answer). This could also be written as (2/3)sqrt(3).

Answer 2

Answer: -2

Explanation:

clockwise past π will put you in the II quadrant. 3/3π plus π/3 = 4π/3.

sec is the reciprocal of cosine. cos π/3 = 1/2. Cosine in the II quadrant is negative. The reciprocal of -1/2 is -2. Therefore 4π/3 clockwise is -2