Question

What is the domain of validity for csc theta = 1 / sin theta?

a. All real numbers
b. All real numbers except odd multiples of pi/ 2
c. All real numbers except even multiples of pi/2
d. All real numbers except multiples of pi.

Answer 1

`De finition\ of\ csc\theta=(1)/(sin\theta)\\-----------------------\\therefore\ csc\theta=(1)/(sin\theta)\to(1)/(sin\theta)=(1)/(sin\theta)\\\\the\ denominator\ must\ be\ different\ from\ zero,\ therefore\\\\sin\theta\\eq0\iff\theta\\eq k\pi\ where\ k\in\mathbb{Z}\\\\Answer:\boxed{D}`