Find remaining five trigonometric functions

Question

Given cos(theta)= 1/5 and theta is not in quadrant 2. Find the remaining five trigonometric functions of theta.

Answer 1

If cos(theta) = 1/5, theta can either be in quadrant 1 or quadrant 4 (it could never be positive in quadrant 2 or 3).

cos(theta)^2 + sin(theta)^2 = 1, so can compute sin(theta) from that. If in quadrant 1, sin(theta) is positive. If in quadrant 4, sin(theta) is negative.

tan(theta) = sin(theta)/cos(theta)

cot(theta) = 1/tan(theta)

sec(theta) = 1/cos(theta)

csc(theta) = 1/sin(theta)