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La ecuación:
Ecuación 3*x^2-x+2=0
Ecuación x^2=-74
Ecuación z^2+z+1=0
Ecuación 90+x-4*10=60
Expresar {x} en función de y en la ecuación:
9*x+14*y=-10
-4*x-8*y=-20
-12*x-10*y=-16
10*x-15*y=16
Expresiones idénticas
dos cos^2(x/ tres)+ tres sin(x/3)= uno
2 coseno de al cuadrado (x dividir por 3) más 3 seno de (x dividir por 3) es igual a 1
dos coseno de al cuadrado (x dividir por tres) más tres seno de (x dividir por 3) es igual a uno
2cos2(x/3)+3sin(x/3)=1
2cos2x/3+3sinx/3=1
2cos²(x/3)+3sin(x/3)=1
2cos en el grado 2(x/3)+3sin(x/3)=1
2cos^2x/3+3sinx/3=1
2cos^2(x dividir por 3)+3sin(x dividir por 3)=1
Expresiones semejantes
2cos^2(x/3)-3sin(x/3)=1

2cos^2(x/3)+3sin(x/3)=1 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

     2/x\        /x\    
2*cos |-| + 3*sin|-| = 1
      \3/        \3/

3 \sin{\left(\frac{x}{3} \right)} + 2 \cos^{2}{\left(\frac{x}{3} \right)} = 1

Simplificar

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Respuesta rápida [src]

         /    /                        _______________\\         /    /                        _______________\\
         |    |        ____     ___   /          ____ ||         |    |        ____     ___   /          ____ ||
         |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||
x1 = 6*re|atan|- - + ------ + ------------------------|| + 6*I*im|atan|- - + ------ + ------------------------||
         \    \  2     2                 2            //         \    \  2     2                 2            //

x_{1} = 6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}

            /                      _______________\
            |      ____     ___   /          ____ |
            |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |
x2 = -6*atan|- + ------ + ------------------------|
            \2     2                 2            /

x_{2} = - 6 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} \right)}

           /    /                      _______________\\         /    /                      _______________\\
           |    |      ____     ___   /          ____ ||         |    |      ____     ___   /          ____ ||
           |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||
x3 = - 6*re|atan|- - ------ + ------------------------|| - 6*I*im|atan|- - ------ + ------------------------||
           \    \2     2                 2            //         \    \2     2                 2            //

x_{3} = - 6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} - 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}

            /                      _______________\
            |      ____     ___   /          ____ |
            |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |
x4 = -6*atan|- + ------ - ------------------------|
            \2     2                 2            /

x_{4} = - 6 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} + \frac{3}{2} + \frac{\sqrt{17}}{2} \right)}

x4 = -6*atan(-sqrt(2)*sqrt(11 + 3*sqrt(17))/2 + 3/2 + sqrt(17)/2)

Suma y producto de raíces [src]

suma

    /    /                        _______________\\         /    /                        _______________\\         /                      _______________\         /    /                      _______________\\         /    /                      _______________\\         /                      _______________\
    |    |        ____     ___   /          ____ ||         |    |        ____     ___   /          ____ ||         |      ____     ___   /          ____ |         |    |      ____     ___   /          ____ ||         |    |      ____     ___   /          ____ ||         |      ____     ___   /          ____ |
    |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |         |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |
6*re|atan|- - + ------ + ------------------------|| + 6*I*im|atan|- - + ------ + ------------------------|| - 6*atan|- + ------ + ------------------------| + - 6*re|atan|- - ------ + ------------------------|| - 6*I*im|atan|- - ------ + ------------------------|| - 6*atan|- + ------ - ------------------------|
    \    \  2     2                 2            //         \    \  2     2                 2            //         \2     2                 2            /         \    \2     2                 2            //         \    \2     2                 2            //         \2     2                 2            /

- 6 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} + \frac{3}{2} + \frac{\sqrt{17}}{2} \right)} + \left(\left(- 6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} - 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}\right) + \left(- 6 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} \right)} + \left(6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}\right)\right)\right)

        /                      _______________\         /                      _______________\       /    /                      _______________\\       /    /                        _______________\\         /    /                      _______________\\         /    /                        _______________\\
        |      ____     ___   /          ____ |         |      ____     ___   /          ____ |       |    |      ____     ___   /          ____ ||       |    |        ____     ___   /          ____ ||         |    |      ____     ___   /          ____ ||         |    |        ____     ___   /          ____ ||
        |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |         |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |       |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||       |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||
- 6*atan|- + ------ + ------------------------| - 6*atan|- + ------ - ------------------------| - 6*re|atan|- - ------ + ------------------------|| + 6*re|atan|- - + ------ + ------------------------|| - 6*I*im|atan|- - ------ + ------------------------|| + 6*I*im|atan|- - + ------ + ------------------------||
        \2     2                 2            /         \2     2                 2            /       \    \2     2                 2            //       \    \  2     2                 2            //         \    \2     2                 2            //         \    \  2     2                 2            //

- 6 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} \right)} - 6 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} + \frac{3}{2} + \frac{\sqrt{17}}{2} \right)} - 6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + 6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} - 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}

producto

/    /    /                        _______________\\         /    /                        _______________\\\        /                      _______________\ /      /    /                      _______________\\         /    /                      _______________\\\        /                      _______________\
|    |    |        ____     ___   /          ____ ||         |    |        ____     ___   /          ____ |||        |      ____     ___   /          ____ | |      |    |      ____     ___   /          ____ ||         |    |      ____     ___   /          ____ |||        |      ____     ___   /          ____ |
|    |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  |||        |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  | |      |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||         |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  |||        |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |
|6*re|atan|- - + ------ + ------------------------|| + 6*I*im|atan|- - + ------ + ------------------------|||*-6*atan|- + ------ + ------------------------|*|- 6*re|atan|- - ------ + ------------------------|| - 6*I*im|atan|- - ------ + ------------------------|||*-6*atan|- + ------ - ------------------------|
\    \    \  2     2                 2            //         \    \  2     2                 2            ///        \2     2                 2            / \      \    \2     2                 2            //         \    \2     2                 2            ///        \2     2                 2            /

\left(6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}\right) \left(- 6 \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} \right)}\right) \left(- 6 \operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} - 6 i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}\right) \left(- 6 \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} + \frac{3}{2} + \frac{\sqrt{17}}{2} \right)}\right)

      /    /    /                        _______________\\     /    /                        _______________\\\ /    /    /                      _______________\\     /    /                      _______________\\\     /                      _______________\     /                      _______________\
      |    |    |        ____     ___   /          ____ ||     |    |        ____     ___   /          ____ ||| |    |    |      ____     ___   /          ____ ||     |    |      ____     ___   /          ____ |||     |      ____     ___   /          ____ |     |      ____     ___   /          ____ |
      |    |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||     |    |  3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||| |    |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  ||     |    |3   \/ 17    \/ 2 *\/  11 - 3*\/ 17  |||     |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |     |3   \/ 17    \/ 2 *\/  11 + 3*\/ 17  |
-1296*|I*im|atan|- - + ------ + ------------------------|| + re|atan|- - + ------ + ------------------------|||*|I*im|atan|- - ------ + ------------------------|| + re|atan|- - ------ + ------------------------|||*atan|- + ------ + ------------------------|*atan|- + ------ - ------------------------|
      \    \    \  2     2                 2            //     \    \  2     2                 2            /// \    \    \2     2                 2            //     \    \2     2                 2            ///     \2     2                 2            /     \2     2                 2            /

- 1296 \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(- \frac{\sqrt{17}}{2} + \frac{3}{2} + \frac{\sqrt{2} \sqrt{11 - 3 \sqrt{17}}}{2} \right)}\right)}\right) \operatorname{atan}{\left(\frac{3}{2} + \frac{\sqrt{17}}{2} + \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} \right)} \operatorname{atan}{\left(- \frac{\sqrt{2} \sqrt{11 + 3 \sqrt{17}}}{2} + \frac{3}{2} + \frac{\sqrt{17}}{2} \right)}

-1296*(i*im(atan(-3/2 + sqrt(17)/2 + sqrt(2)*sqrt(11 - 3*sqrt(17))/2)) + re(atan(-3/2 + sqrt(17)/2 + sqrt(2)*sqrt(11 - 3*sqrt(17))/2)))*(i*im(atan(3/2 - sqrt(17)/2 + sqrt(2)*sqrt(11 - 3*sqrt(17))/2)) + re(atan(3/2 - sqrt(17)/2 + sqrt(2)*sqrt(11 - 3*sqrt(17))/2)))*atan(3/2 + sqrt(17)/2 + sqrt(2)*sqrt(11 + 3*sqrt(17))/2)*atan(3/2 + sqrt(17)/2 - sqrt(2)*sqrt(11 + 3*sqrt(17))/2)

Respuesta numérica [src]

x1 = -19.7033648056729

x2 = -0.853808884134159

x3 = -585.190042451836

x4 = -38.5529207272117

x5 = -95.101588491828

x6 = 74.5444148020209

x7 = 55.6948588804821

x8 = 66.8272546095198

x9 = 10.2785868449035

x10 = -83.9691927627903

x11 = -1791.56162143032

x12 = 17.9957470374046

x13 = 36.8453029589434

x14 = -27.420524998174

x15 = -46.2700809197127

x16 = 47.9776986879811

x17 = 93.3939707235596

x18 = -102.818748684329

x19 = -8.57096907663522

x20 = -65.1196368412515

x21 = 632.313932255683

x22 = -76.2520325702892

x23 = 293.021925667985

x24 = -57.4024766487504

x25 = 85.6768105310586

x26 = 112.243526645098

x27 = 29.1281427664423

x27 = 29.1281427664423

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Expresiones idénticas

Expresiones semejantes

2cos^2(x/3)+3sin(x/3)=1 la ecuación

Solución numérica:

Solución