Solution
Using the trigonometric ratio, SOHCAHTOA
[tex]\begin{gathered} \text{SOH, CAH and TOA respectively represents} \\ \sin e\text{ }\theta=\frac{opposite}{\text{hypothenus}} \\ \cos \theta=\frac{adjacent}{\text{hypothenuse}} \\ \text{Tan}\theta\text{ = }\frac{opposite}{\text{adjacent}} \end{gathered}[/tex]
From the question
[tex]\begin{gathered} \cos \theta=-\frac{5}{13} \\ \text{Therefore } \\ \text{adjacent = 5} \\ hypothenuse\text{ = 13} \end{gathered}[/tex]Using pythagoras theorem, we can find the opposite
so that
[tex]\begin{gathered} \text{Hypothenuse}^2=opposite^2+adjacent^2 \\ 13^2=opposite^2+5^2 \\ opposite\text{ }^2=169-25 \\ \text{opposite =}\sqrt[]{144} \\ \text{opposite = 12} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} \sin e\theta=\frac{opposite}{\text{hypothenuse}} \\ \sin e\theta=\frac{12}{13} \\ \sin ce\text{ the terminal side is in the quadrant II and sine positive in the quadrant II, } \\ Sine\text{ }\theta=\frac{12}{13} \end{gathered}[/tex]Therefore the right answer is option B
