Question

Hi, can you help me to solve this exercise please!

Answer 1

Given that:

$\sin (\theta)=\frac{5}{13}$

And knowing that:

$0\degree<\theta<90\degree$

You need to remember that, by definition:

$\csc \theta=\frac{1}{\sin \theta}$

Therefore, the cosecant of the angle does not exist when:

$\sin \theta=0$

Because the division by zero is not defined.

Therefore, you can conclude that, in this case:

$\csc \theta=\frac{1}{\frac{5}{13}}$

Simplifying, you get:

$\begin{gathered} \csc \theta=\frac{\frac{1}{1}}{\frac{5}{13}} \\ \\ \csc \theta=\frac{1\cdot13}{1\cdot5} \\ \\ \csc \theta=\frac{13}{5} \end{gathered}$

Hence, the answer is:

$\csc \theta=\frac{13}{5}$