Question Number 5857 by FilupSmith last updated on 02/Jun/16
$$\mathrm{tan}\:\theta\:=\:\frac{{b}}{{a}} \\ $$$$\mathrm{For}\:\mathrm{what}\:\mathrm{range}/\mathrm{values}\:\mathrm{of}\:\theta\:\mathrm{gives} \\ $$$${a}\geqslant{b}? \\ $$
Answered by 123456 last updated on 02/Jun/16
![a≥b b≤a (b/a)≤1 tan θ≤1 k∈Z θ∈[2πk∣(π/4)+2πk]∪((π/2)+2πk∣((5π)/4)+2πk]∪(((3π)/2)+2πk∣2π+2πk]](Q5861.png)
$${a}\geqslant{b} \\ $$$${b}\leqslant{a} \\ $$$$\frac{{b}}{{a}}\leqslant\mathrm{1} \\ $$$$\mathrm{tan}\:\theta\leqslant\mathrm{1} \\ $$$${k}\in\mathbb{Z} \\ $$$$\theta\in\left[\mathrm{2}\pi{k}\mid\frac{\pi}{\mathrm{4}}+\mathrm{2}\pi{k}\right]\cup\left(\frac{\pi}{\mathrm{2}}+\mathrm{2}\pi{k}\mid\frac{\mathrm{5}\pi}{\mathrm{4}}+\mathrm{2}\pi{k}\right]\cup\left(\frac{\mathrm{3}\pi}{\mathrm{2}}+\mathrm{2}\pi{k}\mid\mathrm{2}\pi+\mathrm{2}\pi{k}\right] \\ $$