A line in 3-dimensional space makes an angle (0

Question

A line in 3-dimensional space makes an angle $	heta$ ($0<	heta\le\pi/2$) with both the $x$ and $y$ axes. Then the set of all values of $	heta$ is the interval:

Accepted Answer

With $l=m=\cos	heta$ and $l^2+m^2+n^2=1$: $n^2=1-2\cos^2	heta\geq0\implies \cos^2	heta\leq	frac12\implies \cos	heta\leq	frac1{\sqrt2}\implies	heta\geq	frac\pi4$.
Combined with $	heta\leq	frac\pi2$: $	heta\in\left[	frac\pi4,	frac\pi2ight]$.

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