MathDB

\sin\alpha>0,\cos\alpha<0,\sin\frac{\alpha}{3}>\cos\frac{\alpha}{3}

, then the range value of

\frac{\alpha}{3}

\text{(A)}\left(2k\pi+\frac{\pi}{6},2k\pi+\frac{\pi}{3}\right),k\in\mathbb{Z}

\text{(B)}\left(\frac{2k\pi}{3}+\frac{\pi}{6},\frac{2k\pi}{3}+\frac{\pi}{3}\right),k\in\mathbb{Z}

\text{(C)}\left(2k\pi+\frac{5\pi}{6},2k\pi+\pi\right),k\in\mathbb{Z}

\text{(D)}\left(2k\pi+\frac{\pi}{4},2k\pi+\frac{\pi}{3}\right)\cup\left(2k\pi+\frac{5\pi}{6},2k\pi+\pi\right),k\in\mathbb{Z}

Problem Statement