You can use All Students Take Calculus (ASTC) to remember when the trig ratios are positive or negative. ASTC goes with the quadrants. A is All, S is sin, T is tangent, C is cosine, and they are positive in those quadrants.
So ALL (sin, cos, tan) are positive in quadrant I, only sin is positive in quadrant II, only tan is positive in quadrant III, and only cos is positive in quadrant IV.
So it says sin < 0, so sin is negative.
And cos > 0, is cos is positive.
Remembering ASTC, the only quadrant with cos positive is quadrant IV.
