Question

The terminal side of O is in quadrant II and cos 0What is sin ?1313O A. - 12O B.O c. 5O D. 1 / 1

Answer 1

Using the trigonometric ratio, SOHCAHTOA

`\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}`

From the question

`\begin{gathered} \cos \theta=-(5)/(13) \\ \text{Therefore } \\ \text{adjacent = 5} \\ hypothenuse\text{ = 13} \end{gathered}`

Using pythagoras theorem, we can find the opposite

so that

`\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}`

Hence,

`\begin{gathered} \sin e\theta=\frac{opposite}{\text{hypothenuse}} \\ \sin e\theta=(12)/(13) \\ \sin ce\text{ the terminal side is in the quadrant II and sine positive in the quadrant II, } \\ Sine\text{ }\theta=(12)/(13) \end{gathered}`

Therefore the right answer is option B