Answer
$\sin\theta=\frac{\sqrt {5}}{7}$
$\cos\theta=\frac{2\sqrt {11}}{7}$
$\csc\theta=\frac{7\sqrt 5}{5}$
$\sec\theta=\frac{7\sqrt {11}}{22}$
$\tan\theta=\frac{\sqrt {55}}{22}$
$\cot\theta=\frac{2\sqrt {55}}{5}$
Work Step by Step
$\sin\theta=\frac{\sqrt {5}}{7}$
Recall that $\sin^{2}\theta+\cos^{2}\theta=1$
$\implies\cos^{2}\theta=1-\sin^{2}\theta=1-(\frac{\sqrt 5}{7})^{2}=\frac{44}{49}$
$\cos\theta=\pm\sqrt {\frac{44}{49}}=\frac{2\sqrt {11}}{7}$ ($\cos\theta\gt0$ in quadrant I)
$\csc\theta=\frac{1}{\sin\theta}=\frac{7}{\sqrt {5}}=\frac{7\sqrt 5}{5}$
$\sec\theta=\frac{1}{\cos\theta}=\frac{7}{2\sqrt {11}}=\frac{7\sqrt {11}}{22}$
$\tan\theta=\frac{\sin\theta}{\cos\theta}=\frac{\frac{\sqrt 5}{7}}{\frac{2\sqrt {11}}{7}}=\frac{\sqrt 5}{2\sqrt {11}}=\frac{\sqrt {55}}{22}$
$\cot\theta=\frac{1}{\tan\theta}=\frac{22}{\sqrt {55}}=\frac{22\sqrt {55}}{55}=\frac{2\sqrt {55}}{5}$
