You don't have to worry about even/odd, but it may be helpful. What you do need to realize is that you are being asked when the function is negative, not when the function's argument is negative. Thus, is certainly positive, but its sine is negative since .
Originally Posted by tangerine_tomato
For example, let's look at . Just because the 193 is negative doesn't mean the tangent will be. We need to look at the quadrant. Since this is a negative angle, we move clockwise from the x-axis. Go around 193 degrees, and you should see that the angle lies in quadrant II:
So, since and , we have
*** | QUAD I
-180° ------------+-------------- 0°
QUAD III | QUAD IV
Or, you could use the fact that tangent is odd, so , and since is in quadrant III, the tangent will be positive, and then the negative in front makes it negative. Either method works.