Answer
1. $sin1020^\circ= -\frac{\sqrt 3}{2}$
2. $cos1020^\circ= \frac{1}{2}$
3. $tan1020^\circ= -\sqrt 3$
4. $cot1020^\circ= -\frac{\sqrt 3}{3}$
5. $sec1020^\circ= 2$
6. $csc1020^\circ= -\frac{2\sqrt 3}{3}$
Work Step by Step
For $1020^\circ=720^\circ+300^\circ$, it is in quadrant IV with reference angle $\theta=360^\circ-300^\circ=60^\circ$, we have:
1. $sin1020^\circ=-sin60^\circ=-\frac{\sqrt 3}{2}$
2. $cos1020^\circ=cos60^\circ=\frac{1}{2}$
3. $tan1020^\circ=-tan60^\circ=-\sqrt 3$
4. $cot1020^\circ=-cot60^\circ=-\frac{\sqrt 3}{3}$
5. $sec1020^\circ=sec60^\circ=\frac{1}{cos60^\circ}=2$
6. $csc1020^\circ=-csc60^\circ=-\frac{1}{sin60^\circ}=-\frac{2\sqrt 3}{3}$
