# 2010_Question1_c

The given equation factors as (\sin x+\cos x)(\sin x+2\cos x)=0, so we just need to count how many times either factor is zero in the given range. By drawing some graphs, we see that the first factor is zero at x=\frac{3\pi}{4} and x=\frac{7\pi}{4}. The second factor is also zero twice in this range (again, by drawing the graphs of y=\sin x and y=-2\cos x and counting intersection points). Importantly, the intersection points are different from the two previous ones, and so we have 4 in total, i.e. (d).

Can Tim keep up this high form???