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- La ecuación:
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Expresiones idénticas
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- sin(3*x)-sin(2*x)=O
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Expresiones semejantes
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Expresiones con funciones
- Seno sin
- sin(x)-2*x-1=0
- sin(1)/((3*x))=-1
- sin(pi*(x^2+1)/(x^2+11))=1/2
- sin(x)-2sqrt(x)=0
- sin(4*a)+cos(2*a)+sin(2*a)*cos(2*a)=1
- Seno sin
- sin(x)-2*x-1=0
- sin(1)/((3*x))=-1
- sin(pi*(x^2+1)/(x^2+11))=1/2
- sin(x)-2sqrt(x)=0
- sin(4*a)+cos(2*a)+sin(2*a)*cos(2*a)=1
sin(3*x)-sin(2*x)=0 la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
sin(3*x) - sin(2*x) = 0
$$- \sin{\left(2 x \right)} + \sin{\left(3 x \right)} = 0$$
Suma y producto de raíces
[src]
suma
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ____ / ___ | | ____ / ___ ___ ___ / ___ ___ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
9*pi pi |I \/ 10 *\/ 5 + \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 | |I \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 | |I I*\/ 5 \/ 2 *\/ 5 - \/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
- ---- - pi + -- + pi - 2*I*log|- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- + ---------------------| - 2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------| - 2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - 2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------|
5 5 \4 8 4 8 / \ 4 4 8 8 / \4 16 4 16 16 16 / \ 4 16 16 16 4 16 / \ 4 4 16 16 16 16 / \4 4 16 16 16 16 /
$$- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)} + \left(- 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(\left(- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} + \left(\left(\left(\left(- \frac{9 \pi}{5} - \pi\right) + \frac{\pi}{5}\right) + \pi\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right)\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right) - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}\right)\right)$$
=
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ___ ___ / ___ ____ / ___ | | ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ____ / ___ ___ ___ / ___ ___ / ___ ____ / ___ |
8*pi | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 | |I \/ 10 *\/ 5 + \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 | |I I*\/ 5 \/ 2 *\/ 5 - \/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 | |I \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 |
- ---- - 2*I*log|- - - ------- - -------------------- + ---------------------| - 2*I*log|- - --------------------- + ------- + --------------------| - 2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - 2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - 2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------| - 2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------|
5 \ 4 4 8 8 / \4 8 4 8 / \ 4 4 16 16 16 16 / \ 4 16 16 16 4 16 / \4 4 16 16 16 16 / \4 16 4 16 16 16 /
$$- \frac{8 \pi}{5} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
producto
/ ___________ ___________\ / ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\ / ___________ ___________ ___________ ___________\
| ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ____ / ___ | | ____ / ___ ___ ___ / ___ ___ / ___ ____ / ___ | | ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ | | ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
-9*pi pi |I \/ 10 *\/ 5 + \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 | |I \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 | | I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 | | I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 | |I I*\/ 5 \/ 2 *\/ 5 - \/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
0*-----*(-pi)*--*pi*-2*I*log|- - --------------------- + ------- + --------------------|*-2*I*log|- - - ------- - -------------------- + ---------------------|*-2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------|*-2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|*-2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|*-2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------|
5 5 \4 8 4 8 / \ 4 4 8 8 / \4 16 4 16 16 16 / \ 4 16 16 16 4 16 / \ 4 4 16 16 16 16 / \4 4 16 16 16 16 /
$$- 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)} - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)} \pi \frac{\pi}{5} \cdot - \pi 0 \left(- \frac{9 \pi}{5}\right)$$
=
0
$$0$$
0
Respuesta rápida
[src]
x1 = 0
$$x_{1} = 0$$
-9*pi
x2 = -----
5
$$x_{2} = - \frac{9 \pi}{5}$$
x3 = -pi
$$x_{3} = - \pi$$
pi
x4 = --
5
$$x_{4} = \frac{\pi}{5}$$
x5 = pi
$$x_{5} = \pi$$
/ ___________ ___________\
| ____ / ___ ___ ___ / ___ |
|I \/ 10 *\/ 5 + \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 |
x6 = -2*I*log|- - --------------------- + ------- + --------------------|
\4 8 4 8 /
$$x_{6} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
/ ___________ ___________\
| ___ ___ / ___ ____ / ___ |
| I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 |
x7 = -2*I*log|- - - ------- - -------------------- + ---------------------|
\ 4 4 8 8 /
$$x_{7} = - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{8} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{8} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ____ / ___ ___ ___ / ___ ___ / ___ ____ / ___ |
|I \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 |
x8 = -2*I*log|- - --------------------- + ------- + -------------------- + -------------------- + ---------------------|
\4 16 4 16 16 16 /
$$x_{8} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} + \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ / ___ ____ / ___ ____ / ___ ___ ___ / ___ |
| I \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 I*\/ 5 \/ 2 *\/ 5 - \/ 5 |
x9 = -2*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
\ 4 16 16 16 4 16 /
$$x_{9} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} - \frac{i}{4} + \frac{\sqrt{5} i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
| I I*\/ 5 \/ 2 *\/ 5 + \/ 5 \/ 2 *\/ 5 - \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
x10 = -2*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
\ 4 4 16 16 16 16 /
$$x_{10} = - 2 i \log{\left(- \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} - \frac{\sqrt{5} i}{4} - \frac{i}{4} \right)}$$
/ ___________ ___________ ___________ ___________\
| ___ ___ / ___ ___ / ___ ____ / ___ ____ / ___ |
|I I*\/ 5 \/ 2 *\/ 5 - \/ 5 \/ 2 *\/ 5 + \/ 5 \/ 10 *\/ 5 + \/ 5 \/ 10 *\/ 5 - \/ 5 |
x11 = -2*I*log|- - ------- - -------------------- + -------------------- + --------------------- + ---------------------|
\4 4 16 16 16 16 /
$$x_{11} = - 2 i \log{\left(- \frac{\sqrt{2} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{2} \sqrt{\sqrt{5} + 5}}{16} + \frac{\sqrt{10} \sqrt{5 - \sqrt{5}}}{16} + \frac{\sqrt{10} \sqrt{\sqrt{5} + 5}}{16} - \frac{\sqrt{5} i}{4} + \frac{i}{4} \right)}$$
x11 = -2*i*log(-sqrt(2)*sqrt(5 - sqrt(5))/16 + sqrt(2)*sqrt(sqrt(5) + 5)/16 + sqrt(10)*sqrt(5 - sqrt(5))/16 + sqrt(10)*sqrt(sqrt(5) + 5)/16 - sqrt(5)*i/4 + i/4)
Respuesta numérica
[src]
x1 = -97.3893722612836
x2 = -43.9822971502571
x3 = 24.5044226980004
x4 = -25.7610597594363
x5 = 28.2743338823081
x6 = -81.6814089933346
x7 = -15.707963267949
x8 = 72.2566310325652
x9 = -39.5840674352314
x10 = 4.39822971502571
x11 = -96.1327351998477
x12 = 18.2212373908208
x13 = -53.4070751110265
x14 = 11.9380520836412
x15 = 25.1327412287183
x16 = -52.1504380495906
x17 = -9.42477796076938
x18 = 82.3097275240526
x19 = -21.9911485751286
x20 = -11.9380520836412
x21 = -45.867252742411
x22 = -4.39822971502571
x23 = 96.1327351998477
x24 = -19.4778744522567
x25 = -49.6371639267187
x26 = -89.8495498926681
x27 = -72.2566310325652
x28 = 86.0796387083603
x29 = 15.707963267949
x30 = -28.2743338823081
x31 = 14.451326206513
x32 = -62.2035345410779
x33 = 99.9026463841554
x34 = -25.1327412287183
x35 = -1.88495559215388
x36 = 89.8495498926681
x37 = 58.4336233567702
x38 = -29.5309709437441
x39 = -8.16814089933346
x40 = -5.65486677646163
x41 = -87.9645943005142
x42 = 45.867252742411
x43 = 62.2035345410779
x44 = 0.0
x45 = 31.4159265358979
x46 = 98.6460093227195
x47 = -48.3805268652828
x48 = 52.1504380495906
x49 = -76.026542216873
x50 = -65.9734457253857
x51 = 48.3805268652828
x52 = 79.7964534011807
x53 = 6.28318530717959
x54 = 76.026542216873
x55 = -42.0973415581032
x56 = 94.2477796076938
x57 = -63.4601716025138
x58 = 65.9734457253857
x59 = -83.5663645854885
x60 = 38.3274303737955
x61 = 21.9911485751286
x62 = 69.7433569096934
x63 = 78.5398163397448
x64 = -92.3628240155399
x65 = -18.2212373908208
x66 = -99.9026463841554
x67 = 68.4867198482575
x68 = -79.7964534011807
x69 = 87.9645943005142
x70 = -37.6991118430775
x71 = 59.6902604182061
x72 = 55.9203492338983
x73 = -6640.69855115811
x74 = 32.0442450666159
x75 = -55.9203492338983
x76 = 42.0973415581032
x77 = 35.8141562509236
x78 = 43.9822971502571
x79 = -35.8141562509236
x80 = -59.6902604182061
x81 = -69.7433569096934
x82 = -93.6194610769758
x83 = 25.7610597594363
x84 = -75.398223686155
x85 = -69.1150383789755
x86 = 62.8318530717959
x87 = -73.5132680940012
x88 = 92.3628240155399
x89 = 8.16814089933346
x90 = 1.88495559215388
x91 = -86.0796387083603
x92 = -32.0442450666159
x93 = 34.5575191894877
x94 = -10.6814150222053
x94 = -10.6814150222053