Answer
$cos\theta= -\frac{2\sqrt 6}{7}$,
$tan\theta= -\frac{5\sqrt 6}{12}$,
$cot\theta= -\frac{2\sqrt 6}{5}$,
$sec\theta= -\frac{7\sqrt 6}{12}$,
$csc\theta= \frac{7}{5}$.
Work Step by Step
Given $sin\theta=\frac{5}{7}$ and $\theta$ in quadrant II, let $y=5, r=7$, we have $x=-\sqrt {7^2-5^2}=-2\sqrt 6$ and
$cos\theta=\frac{x}{r}=-\frac{2\sqrt 6}{7}$,
$tan\theta=\frac{y}{x}=-\frac{5\sqrt 6}{12}$,
$cot\theta=\frac{1}{tan\theta}=-\frac{2\sqrt 6}{5}$,
$sec\theta=\frac{1}{cos\theta}=-\frac{7\sqrt 6}{12}$,
$csc\theta=\frac{1}{sin\theta}=\frac{7}{5}$.
