Sr Examen
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- La ecuación:
-
Ecuación x^2-6x+9=0
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Ecuación (x-11)^4=(x+3)^4
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Ecuación √(x^2-1)^3=2*x
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Ecuación -x/12+x=55/12
- Expresar {x} en función de y en la ecuación:
- 18*x-11*y=2
- 12*x-14*y=20
- -3*x-20*y=-13
- -16*x+14*y=-9
- Derivada de:
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cos^3(x)
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sin^3(x)
- Integral de d{x}:
- cos^3(x)
- sin^3(x)
- Gráfico de la función y =:
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sin^3(x)
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Expresiones idénticas
- cos^ tres (x)=sin^ tres (x)
- coseno de al cubo (x) es igual a seno de al cubo (x)
- coseno de en el grado tres (x) es igual a seno de en el grado tres (x)
- cos3(x)=sin3(x)
- cos3x=sin3x
- cos³(x)=sin³(x)
- cos en el grado 3(x)=sin en el grado 3(x)
- cos^3x=sin^3x
-
Expresiones con funciones
- Coseno cos
- cos(x)+sin(x)=1
- cos(2*x)=1
- cos(3*x)=0
- cos(-x)=-1
- cos(x)=-0,5
- Seno sin
- sin(x)=-1/5
- sin(3*x-pi/6)=1/2
- sin(x)=-3/2
- sin(x)^3+cos(x)^3=1
- sin(pi*x/3)=1/2
cos^3(x)=sin^3(x) la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
3 3 cos (x) = sin (x)
$$\cos^{3}{\left(x \right)} = \sin^{3}{\left(x \right)}$$
Suma y producto de raíces
[src]
suma
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ pi | |1 I*\/ 3 || | |1 I*\/ 3 || | |1 I*\/ 3 || | |1 I*\/ 3 || -- + - re|atan|- - -------|| - I*im|atan|- - -------|| + - re|atan|- + -------|| - I*im|atan|- + -------|| 4 \ \2 2 // \ \2 2 // \ \2 2 // \ \2 2 //
$$\left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right) + \left(\frac{\pi}{4} + \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right)\right)$$
=
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
| |1 I*\/ 3 || | |1 I*\/ 3 || pi | |1 I*\/ 3 || | |1 I*\/ 3 ||
- re|atan|- + -------|| - re|atan|- - -------|| + -- - I*im|atan|- + -------|| - I*im|atan|- - -------||
\ \2 2 // \ \2 2 // 4 \ \2 2 // \ \2 2 //
$$- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + \frac{\pi}{4} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$
producto
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ pi | | |1 I*\/ 3 || | |1 I*\/ 3 ||| | | |1 I*\/ 3 || | |1 I*\/ 3 ||| --*|- re|atan|- - -------|| - I*im|atan|- - -------|||*|- re|atan|- + -------|| - I*im|atan|- + -------||| 4 \ \ \2 2 // \ \2 2 /// \ \ \2 2 // \ \2 2 ///
$$\frac{\pi}{4} \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
| | |1 I*\/ 3 || | |1 I*\/ 3 ||| | | |1 I*\/ 3 || | |1 I*\/ 3 |||
pi*|I*im|atan|- + -------|| + re|atan|- + -------|||*|I*im|atan|- - -------|| + re|atan|- - -------|||
\ \ \2 2 // \ \2 2 /// \ \ \2 2 // \ \2 2 ///
------------------------------------------------------------------------------------------------------
4
$$\frac{\pi \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}\right)}{4}$$
pi*(i*im(atan(1/2 + i*sqrt(3)/2)) + re(atan(1/2 + i*sqrt(3)/2)))*(i*im(atan(1/2 - i*sqrt(3)/2)) + re(atan(1/2 - i*sqrt(3)/2)))/4
Respuesta rápida
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pi
x1 = --
4
$$x_{1} = \frac{\pi}{4}$$
/ / ___\\ / / ___\\
| |1 I*\/ 3 || | |1 I*\/ 3 ||
x2 = - re|atan|- - -------|| - I*im|atan|- - -------||
\ \2 2 // \ \2 2 //
$$x_{2} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} - \frac{\sqrt{3} i}{2} \right)}\right)}$$
/ / ___\\ / / ___\\
| |1 I*\/ 3 || | |1 I*\/ 3 ||
x3 = - re|atan|- + -------|| - I*im|atan|- + -------||
\ \2 2 // \ \2 2 //
$$x_{3} = - \operatorname{re}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{atan}{\left(\frac{1}{2} + \frac{\sqrt{3} i}{2} \right)}\right)}$$
x3 = -re(atan(1/2 + sqrt(3)*i/2)) - i*im(atan(1/2 + sqrt(3)*i/2))
Respuesta numérica
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x1 = -115.453530019425
x2 = -46.3384916404494
x3 = -90.3207887907066
x4 = -36.9137136796801
x5 = -77.7544181763474
x6 = 3.92699081698724
x7 = -18.0641577581413
x8 = -84.037603483527
x9 = 54.1924732744239
x10 = 126.449104306989
x11 = 19.6349540849362
x12 = -633.816317861741
x13 = -756.338431351743
x14 = 38.484510006475
x15 = -11.7809724509617
x16 = 69.9004365423729
x17 = 88.7499924639117
x18 = -62.0464549083984
x19 = -2.35619449019234
x20 = 107.59954838545
x21 = 32.2013246992954
x22 = -49.4800842940392
x23 = -5.49778714378214
x24 = 57.3340659280137
x25 = 10.2101761241668
x26 = 60.4756585816035
x27 = -71.4712328691678
x28 = -27.4889357189107
x29 = 76.1836218495525
x30 = 82.4668071567321
x31 = -80.8960108299372
x32 = 63.6172512351933
x33 = -24.3473430653209
x34 = -335.36501577071
x35 = -14450.5408083497
x36 = 16.4933614313464
x37 = -55.7632696012188
x38 = -93.4623814442964
x39 = 85.6083998103219
x40 = -40.0553063332699
x41 = 29.0597320457056
x42 = 41.6261026600648
x43 = 25.9181393921158
x44 = 98.174770424681
x45 = -33.7721210260903
x46 = 47.9092879672443
x47 = -68.329640215578
x48 = 91.8915851175014
x49 = -99.7455667514759
x50 = 51.0508806208341
x50 = 51.0508806208341