Question

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

Answer 1

Given that:

`\sin (\theta)=(5)/(13)`

And knowing that:

`0\degree<\theta<90\degree`

You need to remember that, by definition:

`\csc \theta=(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=(1)/((5)/(13))`

Simplifying, you get:

`\begin{gathered} \csc \theta=((1)/(1))/((5)/(13)) \\ \\ \csc \theta=(1\cdot13)/(1\cdot5) \\ \\ \csc \theta=(13)/(5) \end{gathered}`

Hence, the answer is:

`\csc \theta=(13)/(5)`