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).