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
1. $\theta = 1020^{\circ}$
The angle lies in the IV quadrant and reference angle is $60^{\circ}$ because $3\times 360^{\circ} - 1020 = 60$
2. In IV quadrant $cos\theta $ and $\sec\theta$ are positive, and remaining functions will be negative
3. $\sin\theta = -sin 60^{\circ} = \frac{-\sqrt 3}{2}$
$\cos\theta =cos 60^{\circ} = \frac{1}{2}$
$\tan\theta =-\tan 60^{\circ} = -\sqrt 3$
$\csc\theta =-\csc 60^{\circ} = \frac{-2\sqrt 3}{3}$
$\sec\theta = \sec 60^{\circ} = 2$
$\cot\theta = -\cot 60^{\circ} = \frac{-\sqrt 3}{3}$
