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Resolver desigualdades/ ctg*x/2-2/3*sin(x)>=0

ctg*x/2-2/3*sin(x)>=0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
cot(x)   2*sin(x)     
------ - -------- >= 0
  2         3
−2sin⁡(x)3+cot⁡(x)2≥0- \frac{2 \sin{\left(x \right)}}{3} + \frac{\cot{\left(x \right)}}{2} \geq 0 
-2*sin(x)/3 + cot(x)/2 >= 0
Respuesta rápida [src] 
  /   /         /       ___      \       \     /           /       ___      \               \\
  |   |         |     \/ 6       |       |     |           |     \/ 6       |               ||
Or|And|x <= atan|----------------|, 0 < x|, And|x <= - atan|----------------| + 2*pi, pi < x||
  |   |         |   _____________|       |     |           |   _____________|               ||
  |   |         |  /        ____ |       |     |           |  /        ____ |               ||
  \   \         \\/  -3 + \/ 73  /       /     \           \\/  -3 + \/ 73  /               //
(x≤atan⁡(6−3+73)∧0<x)∨(x≤−atan⁡(6−3+73)+2π∧π<x)\left(x \leq \operatorname{atan}{\left(\frac{\sqrt{6}}{\sqrt{-3 + \sqrt{73}}} \right)} \wedge 0 < x\right) \vee \left(x \leq - \operatorname{atan}{\left(\frac{\sqrt{6}}{\sqrt{-3 + \sqrt{73}}} \right)} + 2 \pi \wedge \pi < x\right) 
((0 < x)∧(x <= atan(sqrt(6)/sqrt(-3 + sqrt(73)))))∨((pi < x)∧(x <= -atan(sqrt(6)/sqrt(-3 + sqrt(73))) + 2*pi))
Respuesta rápida 2 [src] 
        /       ___      \               /       ___      \        
        |     \/ 6       |               |     \/ 6       |        
(0, atan|----------------|] U (pi, - atan|----------------| + 2*pi]
        |   _____________|               |   _____________|        
        |  /        ____ |               |  /        ____ |        
        \\/  -3 + \/ 73  /               \\/  -3 + \/ 73  /
x in (0,atan⁡(6−3+73)]∪(π,−atan⁡(6−3+73)+2π]x\ in\ \left(0, \operatorname{atan}{\left(\frac{\sqrt{6}}{\sqrt{-3 + \sqrt{73}}} \right)}\right] \cup \left(\pi, - \operatorname{atan}{\left(\frac{\sqrt{6}}{\sqrt{-3 + \sqrt{73}}} \right)} + 2 \pi\right] 
x in Union(Interval.Lopen(0, atan(sqrt(6)/sqrt(-3 + sqrt(73)))), Interval.Lopen(pi, -atan(sqrt(6)/sqrt(-3 + sqrt(73))) + 2*pi))
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