If [x] denotes the greatest integer x, then the system of linear equations []x+[-]y=0, []x…

Question

If $[x]$ denotes the greatest integer $\le x$, then the system of linear equations $[\sin	heta]x+[-\cos	heta]y=0$, $[\cot	heta]x+y=0$:

Accepted Answer

Case $	heta\in\left(	frac\pi2,	frac{2\pi}3ight)$: $[\sin	heta]=0,\ [-\cos	heta]=0,\ [\cot	heta]=-1$. The system becomes $0\cdot x+0\cdot y=0$ and $-x+y=0$ --- infinitely many solutions.

Case $	heta\in\left(\pi,	frac{7\pi}6ight)$: $[\sin	heta]=-1,\ [-\cos	heta]=0$. The system becomes $-x+0\cdot y=0$ (so $x=0$) and $[\cot	heta]x+y=0$ (so $y=0$) --- the unique solution $x=y=0$.

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