Trigonometry Odd Even Question?

I'm not student, but reading a Trig book which has some wrong answers. Here is one below, I will give you the question, then the answer. Tell me if it is right or wrong, then please tell me why its right or wrong:

Q. If csc z = 17/8 and cos z = -15/17, find cot z?

A. If csc z = 17/8 and cos z = -15/17, then sin z = 8/17 and tan z = - 8/15. Therefore cot z = -15/8

My book doesnt explain certain thing well enough, so I usually try to find patterns, or search through the internet to find my answers. The odd even trig functions shouldnt be hard, but I cant reconcile these.

Shouldnt the positive fraction, csc z, mean cot z would be positive also since both are odd functions (tan z also) and the even function, cos z, is negative? If not, explain why or please tell me where to go.