In which quadrants do sine and cosine have the opposite sign?
In second and fourth quadrants, sine and cosine have opposite sign.
Trigonometric functions sine and cosine are both positive in first quadrant but in third quadrant both are negative. Hence in these two quadrants they have same sign.
However, in second quadrant while sine is positive, cosine is negative. And in fourth quadrant, cosine is positive and sine is negative.
Hence, in second and fourth quadrants, they have opposite sign.