4. (2006 National High School Mathematics League Shaanxi Province Preliminary Test) If $\sin ^{3} \theta-\cos ^{3} \theta \geqslant \cos \theta-\sin \theta, 0 \leqslant \theta<2 \pi$, then the range of angle 0 is
A. $\left[0, \frac{\pi}{4}\right]$
B. $\left[\frac{\pi}{4}, \pi\right]$
C. $\left[\frac{\pi}{4}, \frac{5 \pi}{4}\right]$
D. $\left[\frac{\pi}{2}, \frac{3 \pi}{2}\right)$
4. C From $\sin ^{3} \theta-\cos ^{3} \theta \geqslant \cos \theta-\sin \theta$, we get $(\sin \theta-\cos \theta)\left(2+\frac{1}{2} \sin ^{2} \theta\right) \geqslant 0$. Since $2+\frac{1}{2} \sin ^{2} \theta>0$, it follows that $\sin \theta-\cos \theta \geqslant 0$. Solving this, we get $\frac{\pi}{4} \leqslant \theta \leqslant \frac{5 \pi}{4}$.