Answer
$sin\theta= -\frac{\sqrt {3}}{2}$,
$cos\theta= \frac{1}{2}$,
$tan\theta= -\sqrt {3}$,
$cot\theta= -\frac{\sqrt {3}}{3}$,
$csc\theta= -\frac{2\sqrt {3}}{3}$.
Work Step by Step
Given $sec\theta=2$, let $r=2, x=1$, we can get $y=\sqrt {r^2-x^2}=\sqrt {3}$. Use the fact that $sin\theta\lt0,cos\theta=\frac{1}{sec\theta}\gt0\longrightarrow \theta$ is in quadrant IV to determine the sign of each function:
$sin\theta=-\frac{y}{r}=-\frac{\sqrt {3}}{2}$,
$cos\theta=\frac{x}{r}=\frac{1}{2}$,
$tan\theta=-\frac{y}{x}=-\sqrt {3}$,
$cot\theta=-\frac{x}{y}=-\frac{\sqrt {3}}{3}$,
$csc\theta=-\frac{r}{y}=-\frac{2\sqrt {3}}{3}$.
