Question

For what value of Θ is cscΘ undefined?0°180°270° II only I and II only I and III only I, II, and III

Answer 1

$I\: and\: II\: only$

1) In this problem, we need to keep in mind that the cosecant is reciprocal to the sine function.

2) Thus, we can write out the following:

$\begin{gathered} csc(\theta)=\frac{1}{\sin (\theta)} \\ \csc (0)=\frac{1}{\sin (0)}=\frac{1}{0}=Undefined \\ \csc (180)=\frac{1}{\sin (180)}=\frac{1}{0}=Undefined \\ \csc (270)=\frac{1}{\sin (270)}=\frac{1}{-1}=-1 \end{gathered}$

Note that we have then undefinition, for no number can be divided by 0.

The answer is:

$I\: and\: II\: only$