Answer
$\sin\theta=\frac{2}{\sqrt {53}}$, $\sec \theta=\frac{\sqrt {53}}{7}$ and $\cot \theta=\frac{7}{2}$
Work Step by Step
$\cot \theta=\frac{1}{\tan\theta}=\frac{7}{2}$
$\sec^{2}\theta =1+\tan^{2}\theta=1+\frac{4}{49}=\frac{53}{49}$
$\implies \sec \theta=\frac{\sqrt {53}}{7}$ ($\sec \theta$ is positive as $0\leq\theta\lt\frac{\pi}{2}$)
$\csc^{2}\theta=1+\cot^{2}\theta=1+\frac{49}{4}=\frac{53}{4}$
$\implies \csc\theta= \frac{\sqrt {53}}{2}$
$\sin\theta= \frac{1}{\csc\theta}=\frac{2}{\sqrt {53}}$
