Answer
$sin ~\theta = -\frac{\sqrt{3}}{2}$
$cos ~\theta = \frac{1}{2}$
$tan ~\theta = -\sqrt{3}$
$csc ~\theta = -\frac{2\sqrt{3}}{3}$
$sec ~\theta = 2$
$cot ~\theta = -\frac{\sqrt{3}}{3}$
Work Step by Step
$1020^{\circ}-(2)(360^{\circ}) = 300^{\circ} = 360^{\circ}-60^{\circ}$
The angle $1020^{\circ}$ makes an angle of $60^{\circ}$ below the positive x-axis. We can let $x=1$ and $y=-\sqrt{3}$. Then $r = 2$.
We can find the values of the six trigonometric functions:
$sin ~\theta = \frac{y}{r} = \frac{-\sqrt{3}}{2}$
$cos ~\theta = \frac{x}{r} = \frac{1}{2}$
$tan ~\theta = \frac{y}{x} = \frac{-\sqrt{3}}{1} = -\sqrt{3}$
$csc ~\theta = \frac{r}{y} = \frac{2}{-\sqrt{3}} = -\frac{2\sqrt{3}}{3}$
$sec ~\theta = \frac{r}{x} = \frac{2}{1} = 2$
$cot ~\theta = \frac{x}{y} = \frac{1}{-\sqrt{3}} = -\frac{\sqrt{3}}{3}$
