Question

Use even and odd properties of the trigonometric functions to find the exact value of the expression. csc(−π/6)

Answer 1

Recall that the reciprocal of the csc function is the sin function, which is an odd function. The angle -pi/6 has its terminal side in Quadrant 4, for which the opposite side is negative, important in determining the sign of csc(-pi/6).

sin(-pi/6) = - sin(pi/6) = -1/2.

Thus, csc(-pi/6) = -1 / (-1/2), or +2 (answer)