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Resolver desigualdades/ sin^2x/3-cos*2x/3<0

sin^2x/3-cos*2x/3<0 desigualdades

En la desigualdad la incógnita

Solución

Ha introducido [src] 
   2                  
sin (x)   cos(2*x)    
------- - -------- < 0
   3         3
sin⁡2(x)3−cos⁡(2x)3<0\frac{\sin^{2}{\left(x \right)}}{3} - \frac{\cos{\left(2 x \right)}}{3} < 0 
sin(x)^2/3 - cos(2*x)/3 < 0
Solución de la desigualdad en el gráfico
0-70-60-50-40-30-20-10102030405060701-1
Respuesta rápida [src] 
  /   /               /      /   /    /    ___\\\                                                        \\     /              /  /      /   /    /    ___\\\       \                                                        \    \     /       /  /         /   /    /    ___\\\\                                                        \     /  /         /   /    /    ___\\\\                                                        \    \\
  |   |               |      |   |atan\2*\/ 2 /||      /     ___________________________________________\||     |              |  |      |   |atan\2*\/ 2 /||       |      /     ___________________________________________\|    |     |       |  |         |   |atan\2*\/ 2 /|||      /     ___________________________________________\|     |  |         |   |atan\2*\/ 2 /|||      /     ___________________________________________\|    ||
  |   |               |      |sin|-------------||      |    /     /    /    ___\\       /    /    ___\\ |||     |              |  |      |sin|-------------||       |      |    /     /    /    ___\\       /    /    ___\\ ||    |     |       |  |         |sin|-------------|||      |    /     /    /    ___\\       /    /    ___\\ ||     |  |         |sin|-------------|||      |    /     /    /    ___\\       /    /    ___\\ ||    ||
  |   |               |      |   \      2      /|      |   /     2|atan\2*\/ 2 /|      2|atan\2*\/ 2 /| |||     |              |  |      |   \      2      /|       |      |   /     2|atan\2*\/ 2 /|      2|atan\2*\/ 2 /| ||    |     |       |  |         |   \      2      /||      |   /     2|atan\2*\/ 2 /|      2|atan\2*\/ 2 /| ||     |  |         |   \      2      /||      |   /     2|atan\2*\/ 2 /|      2|atan\2*\/ 2 /| ||    ||
Or|And|0 <= x, x < -I*|I*atan|------------------| + log|  /   cos |-------------| + sin |-------------| |||, And|x <= 2*pi, -I*|I*|- atan|------------------| + 2*pi| + log|  /   cos |-------------| + sin |-------------| || < x|, And|x < -I*|I*|pi + atan|------------------|| + log|  /   cos |-------------| + sin |-------------| ||, -I*|I*|pi - atan|------------------|| + log|  /   cos |-------------| + sin |-------------| || < x||
  |   |               |      |   /    /    ___\\|      \\/        \      2      /       \      2      / /||     |              |  |      |   /    /    ___\\|       |      \\/        \      2      /       \      2      / /|    |     |       |  |         |   /    /    ___\\||      \\/        \      2      /       \      2      / /|     |  |         |   /    /    ___\\||      \\/        \      2      /       \      2      / /|    ||
  |   |               |      |   |atan\2*\/ 2 /||                                                        ||     |              |  |      |   |atan\2*\/ 2 /||       |                                                        |    |     |       |  |         |   |atan\2*\/ 2 /|||                                                        |     |  |         |   |atan\2*\/ 2 /|||                                                        |    ||
  |   |               |      |cos|-------------||                                                        ||     |              |  |      |cos|-------------||       |                                                        |    |     |       |  |         |cos|-------------|||                                                        |     |  |         |cos|-------------|||                                                        |    ||
  \   \               \      \   \      2      //                                                        //     \              \  \      \   \      2      //       /                                                        /    /     \       \  \         \   \      2      ///                                                        /     \  \         \   \      2      ///                                                        /    //
(0≤x∧x<−i(log⁡(sin⁡2(atan⁡(22)2)+cos⁡2(atan⁡(22)2))+iatan⁡(sin⁡(atan⁡(22)2)cos⁡(atan⁡(22)2))))∨(x≤2π∧−i(log⁡(sin⁡2(atan⁡(22)2)+cos⁡2(atan⁡(22)2))+i(−atan⁡(sin⁡(atan⁡(22)2)cos⁡(atan⁡(22)2))+2π))<x)∨(x<−i(log⁡(sin⁡2(atan⁡(22)2)+cos⁡2(atan⁡(22)2))+i(atan⁡(sin⁡(atan⁡(22)2)cos⁡(atan⁡(22)2))+π))∧−i(log⁡(sin⁡2(atan⁡(22)2)+cos⁡2(atan⁡(22)2))+i(π−atan⁡(sin⁡(atan⁡(22)2)cos⁡(atan⁡(22)2))))<x)\left(0 \leq x \wedge x < - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)} + i \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)}\right)\right) \vee \left(x \leq 2 \pi \wedge - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)} + i \left(- \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)} + 2 \pi\right)\right) < x\right) \vee \left(x < - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)} + i \left(\operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)} + \pi\right)\right) \wedge - i \left(\log{\left(\sqrt{\sin^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)} + \cos^{2}{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)} + i \left(\pi - \operatorname{atan}{\left(\frac{\sin{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}}{\cos{\left(\frac{\operatorname{atan}{\left(2 \sqrt{2} \right)}}{2} \right)}} \right)}\right)\right) < x\right) 
((0 <= x)∧(x < -i*(i*atan(sin(atan(2*sqrt(2))/2)/cos(atan(2*sqrt(2))/2)) + log(sqrt(cos(atan(2*sqrt(2))/2)^2 + sin(atan(2*sqrt(2))/2)^2)))))∨((x <= 2*pi)∧(-i*(i*(-atan(sin(atan(2*sqrt(2))/2)/cos(atan(2*sqrt(2))/2)) + 2*pi) + log(sqrt(cos(atan(2*sqrt(2))/2)^2 + sin(atan(2*sqrt(2))/2)^2))) < x))∨((x < -i*(i*(pi + atan(sin(atan(2*sqrt(2))/2)/cos(atan(2*sqrt(2))/2))) + log(sqrt(cos(atan(2*sqrt(2))/2)^2 + sin(atan(2*sqrt(2))/2)^2))))∧(-i*(i*(pi - atan(sin(atan(2*sqrt(2))/2)/cos(atan(2*sqrt(2))/2))) + log(sqrt(cos(atan(2*sqrt(2))/2)^2 + sin(atan(2*sqrt(2))/2)^2))) < x))
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