Explanation:
Given that:
[tex]\begin{gathered} \theta=? \\ Hypotenuse=6 \\ Adjacent=5 \end{gathered}[/tex]
We will obtain the following trigonometric identities as shown below:
[tex]\begin{gathered} csc\theta=\frac{1}{\sin\theta} \\ \text{Using Pythagoras Theorem, we will obtain the missing side:} \\ a^2=c^2-b^2 \\ a^2=6^2-5^2 \\ a^2=36-25 \\ a^2=11 \\ a=\sqrt{11} \\ a=opposite=\sqrt{11} \\ \\ \sin\theta=\frac{opposite}{hypotenuse}=\frac{\sqrt{11}}{6} \\ csc\theta=\frac{1}{\frac{\sqrt{11}}{6}}=\frac{6}{\sqrt{11}} \\ csc\theta=\frac{6}{\sqrt{11}} \end{gathered}[/tex]
Then,
[tex]\begin{gathered} cot\theta=\frac{1}{\tan\theta} \\ \tan\theta=\frac{opposite}{adjacent}=\frac{\sqrt{11}}{5} \\ cot\theta=\frac{1}{\frac{\sqrt{11}}{5}} \\ cot\theta=\frac{5}{\sqrt{11}} \end{gathered}[/tex]
Then,
[tex]\sin\theta=\frac{\sqrt{11}}{6}[/tex]
