Find the values of the 6 trig functions of alpha if secalpha

Find the values of the 6 trig functions of alpha if sec(alpha) = -13/5 and alpha is located in Q. III.

Given

is in III quadrant. So tan and cot will be +ve only.

sec = -13/5

cos = 1/sec = -5/13

tan = sqrt(sec^2 - 1) = sqrt[(169/25) - 1] = 12/5

cot = 1/tan = 5/12

sin = sqrt[1 - cos^2 ] = sqrt[1 - (25/169)] = -12/13

csc = 1/sin = -13/12