How to draw a right angled triangle for determining trig ratios of a reflex angle? Which of the two is correct?

Question

So the two options are:-

The circle here is a unit circle and the two reflex angles of the two figures are equal.

If there's any problem in my question, please inform me. Thanks a lot.

Answer 1

Either way, you will need to reduce the angle to an angle in the $\left\lbrack-\frac{\pi}{2},\,\frac{\pi}{2}\right\rbrack$ range. I find that it is easiest to look at a similar angle in the first quadrant, and then change the sign of the sine or cosine as needed. Basically:

• If $\theta$ is in quadrant II, look at $\pi-\theta$ and negate cosine.
• If $\theta$ is in quadrant III, look at $\theta-\pi$ and negate sine and cosine.
• If $\theta$ is in quadrant IV, look at $-\theta$ and negate sine.