Sr Examen

Otras calculadoras

cosx*cos2x*cos4x=0.125 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

v

Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
cos(x)*cos(2*x)*cos(4*x) = 1/8
cos⁡(x)cos⁡(2x)cos⁡(4x)=18\cos{\left(x \right)} \cos{\left(2 x \right)} \cos{\left(4 x \right)} = \frac{1}{8}
Simplificar
Gráfica
0-80-60-40-2020406080-1001002-2
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Suma y producto de raíces [src] 
suma
                                                                                                                                  /   /pi\\            /   /pi\\                                                                                   /   /pi\\            /   /pi\\                                   
                                                                                                /    _____________________\       |cos|--||            |cos|--||        /    _____________________\              /    _____________________\       |cos|--||            |cos|--||        /    _____________________\
  pi   2*pi   pi   pi   2*pi   pi   7*pi   6*pi        / 7 ____\        /     2/9\              |   /    2/pi\      2/pi\ |       |   \18/|            |   \18/|        |   /    2/pi\      2/pi\ |              |   /    2/pi\      2/pi\ |       |   \14/|            |   \14/|        |   /    2/pi\      2/pi\ |
- -- - ---- - -- + -- + ---- + -- + ---- + ---- - I*log\-\/ -1 / - I*log\-(-1)   / + -pi - I*log|  /  cos |--| + sin |--| | + atan|-------| + pi - atan|-------| - I*log|  /  cos |--| + sin |--| | + -pi - I*log|  /  cos |--| + sin |--| | + atan|-------| + pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
  3     7     9    9     7     3     9      7                                                   \\/       \18/       \18/ /       |   /pi\|            |   /pi\|        \\/       \18/       \18/ /              \\/       \14/       \14/ /       |   /pi\|            |   /pi\|        \\/       \14/       \14/ /
                                                                                                                                  |sin|--||            |sin|--||                                                                                   |sin|--||            |sin|--||                                   
                                                                                                                                  \   \18//            \   \18//                                                                                   \   \14//            \   \14//
((−π−ilog⁡(sin⁡2(π14)+cos⁡2(π14))+atan⁡(cos⁡(π14)sin⁡(π14)))+(((−π−ilog⁡(sin⁡2(π18)+cos⁡2(π18))+atan⁡(cos⁡(π18)sin⁡(π18)))+(−ilog⁡(−(−1)29)+(−ilog⁡(−−17)+(((((((−π3−2π7)−π9)+π9)+2π7)+π3)+7π9)+6π7))))+(−atan⁡(cos⁡(π18)sin⁡(π18))−ilog⁡(sin⁡2(π18)+cos⁡2(π18))+π)))+(−atan⁡(cos⁡(π14)sin⁡(π14))−ilog⁡(sin⁡2(π14)+cos⁡2(π14))+π)\left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}\right) + \left(\left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right) + \left(- i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} + \left(- i \log{\left(- \sqrt[7]{-1} \right)} + \left(\left(\left(\left(\left(\left(\left(- \frac{\pi}{3} - \frac{2 \pi}{7}\right) - \frac{\pi}{9}\right) + \frac{\pi}{9}\right) + \frac{2 \pi}{7}\right) + \frac{\pi}{3}\right) + \frac{7 \pi}{9}\right) + \frac{6 \pi}{7}\right)\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \pi\right)\right)\right) + \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi\right) 
=
                                                   /    _____________________\          /    _____________________\
103*pi        / 7 ____\        /     2/9\          |   /    2/pi\      2/pi\ |          |   /    2/pi\      2/pi\ |
------ - I*log\-\/ -1 / - I*log\-(-1)   / - 2*I*log|  /  cos |--| + sin |--| | - 2*I*log|  /  cos |--| + sin |--| |
  63                                               \\/       \14/       \14/ /          \\/       \18/       \18/ /
−ilog⁡(−−17)−ilog⁡(−(−1)29)−2ilog⁡(sin⁡2(π14)+cos⁡2(π14))−2ilog⁡(sin⁡2(π18)+cos⁡2(π18))+103π63- i \log{\left(- \sqrt[7]{-1} \right)} - i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} - 2 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \frac{103 \pi}{63} 
producto
                                                                          /                                             /   /pi\\\ /         /   /pi\\                                   \ /                                             /   /pi\\\ /         /   /pi\\                                   \
                                                                          |           /    _____________________\       |cos|--||| |         |cos|--||        /    _____________________\| |           /    _____________________\       |cos|--||| |         |cos|--||        /    _____________________\|
-pi  -2*pi -pi  pi 2*pi pi 7*pi 6*pi /      / 7 ____\\ /      /     2/9\\ |           |   /    2/pi\      2/pi\ |       |   \18/|| |         |   \18/|        |   /    2/pi\      2/pi\ || |           |   /    2/pi\      2/pi\ |       |   \14/|| |         |   \14/|        |   /    2/pi\      2/pi\ ||
----*-----*----*--*----*--*----*----*\-I*log\-\/ -1 //*\-I*log\-(-1)   //*|-pi - I*log|  /  cos |--| + sin |--| | + atan|-------||*|pi - atan|-------| - I*log|  /  cos |--| + sin |--| ||*|-pi - I*log|  /  cos |--| + sin |--| | + atan|-------||*|pi - atan|-------| - I*log|  /  cos |--| + sin |--| ||
 3     7    9   9   7   3   9    7                                        |           \\/       \18/       \18/ /       |   /pi\|| |         |   /pi\|        \\/       \18/       \18/ /| |           \\/       \14/       \14/ /       |   /pi\|| |         |   /pi\|        \\/       \14/       \14/ /|
                                                                          |                                             |sin|--||| |         |sin|--||                                   | |                                             |sin|--||| |         |sin|--||                                   |
                                                                          \                                             \   \18/// \         \   \18//                                   / \                                             \   \14/// \         \   \14//                                   /
−ilog⁡(−(−1)29)−ilog⁡(−−17)6π77π9π32π7π9⋅−π9⋅−π3(−2π7)(−π−ilog⁡(sin⁡2(π18)+cos⁡2(π18))+atan⁡(cos⁡(π18)sin⁡(π18)))(−atan⁡(cos⁡(π18)sin⁡(π18))−ilog⁡(sin⁡2(π18)+cos⁡2(π18))+π)(−π−ilog⁡(sin⁡2(π14)+cos⁡2(π14))+atan⁡(cos⁡(π14)sin⁡(π14)))(−atan⁡(cos⁡(π14)sin⁡(π14))−ilog⁡(sin⁡2(π14)+cos⁡2(π14))+π)- i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} - i \log{\left(- \sqrt[7]{-1} \right)} \frac{6 \pi}{7} \frac{7 \pi}{9} \frac{\pi}{3} \frac{2 \pi}{7} \frac{\pi}{9} \cdot - \frac{\pi}{9} \cdot - \frac{\pi}{3} \left(- \frac{2 \pi}{7}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \pi\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi\right) 
=
       12    / 7 ____\    /     2/9\
3200*pi  *log\-\/ -1 /*log\-(-1)   /
------------------------------------
             425329947
3200π12log⁡(−−17)log⁡(−(−1)29)425329947\frac{3200 \pi^{12} \log{\left(- \sqrt[7]{-1} \right)} \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)}}{425329947} 
3200*pi^12*log(-(-1)^(1/7))*log(-(-1)^(2/9))/425329947
Respuesta rápida [src] 
     -pi 
x1 = ----
      3
x1=−π3x_{1} = - \frac{\pi}{3} 
     -2*pi
x2 = -----
       7
x2=−2π7x_{2} = - \frac{2 \pi}{7} 
     -pi 
x3 = ----
      9
x3=−π9x_{3} = - \frac{\pi}{9} 
     pi
x4 = --
     9
x4=π9x_{4} = \frac{\pi}{9} 
     2*pi
x5 = ----
      7
x5=2π7x_{5} = \frac{2 \pi}{7} 
     pi
x6 = --
     3
x6=π3x_{6} = \frac{\pi}{3} 
     7*pi
x7 = ----
      9
x7=7π9x_{7} = \frac{7 \pi}{9} 
     6*pi
x8 = ----
      7
x8=6π7x_{8} = \frac{6 \pi}{7} 
           / 7 ____\
x9 = -I*log\-\/ -1 /
x9=−ilog⁡(−−17)x_{9} = - i \log{\left(- \sqrt[7]{-1} \right)} 
            /     2/9\
x10 = -I*log\-(-1)   /
x10=−ilog⁡(−(−1)29)x_{10} = - i \log{\left(- \left(-1\right)^{\frac{2}{9}} \right)} 
                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \18/|
x11 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \18/       \18/ /       |   /pi\|
                                                   |sin|--||
                                                   \   \18//
x11=−π−ilog⁡(sin⁡2(π18)+cos⁡2(π18))+atan⁡(cos⁡(π18)sin⁡(π18))x_{11} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} 
               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \18/|        |   /    2/pi\      2/pi\ |
x12 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \18/       \18/ /
               |sin|--||                                   
               \   \18//
x12=−atan⁡(cos⁡(π18)sin⁡(π18))−ilog⁡(sin⁡2(π18)+cos⁡2(π18))+πx_{12} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{18} \right)}}{\sin{\left(\frac{\pi}{18} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{18} \right)} + \cos^{2}{\left(\frac{\pi}{18} \right)}} \right)} + \pi 
                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \14/|
x13 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \14/       \14/ /       |   /pi\|
                                                   |sin|--||
                                                   \   \14//
x13=−π−ilog⁡(sin⁡2(π14)+cos⁡2(π14))+atan⁡(cos⁡(π14)sin⁡(π14))x_{13} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} 
               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \14/|        |   /    2/pi\      2/pi\ |
x14 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \14/       \14/ /
               |sin|--||                                   
               \   \14//
x14=−atan⁡(cos⁡(π14)sin⁡(π14))−ilog⁡(sin⁡2(π14)+cos⁡2(π14))+πx_{14} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{14} \right)}}{\sin{\left(\frac{\pi}{14} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{14} \right)} + \cos^{2}{\left(\frac{\pi}{14} \right)}} \right)} + \pi 
x14 = -atan(cos(pi/14)/sin(pi/14)) - i*log(sqrt(sin(pi/14)^2 + cos(pi/14)^2)) + pi
Respuesta numérica [src] 
x1 = 61.9342551707702
x2 = 45.0294947014537
x3 = 85.2718005974372
x4 = -91.8043186549017
x5 = 68.2174404779498
x6 = 35.9537825910832
x7 = 98.0875039620813
x8 = -13.4639685153848
x9 = -43.6332312998582
x10 = 49.9164166070378
x11 = -65.2753140245879
x12 = 0.349065850398866
x13 = -1.74532925199433
x14 = -26.030339129744
x15 = -11.6687727133335
x16 = -9.87357691128221
x17 = 27.5762021815104
x18 = 63.8790506229925
x19 = -3.83972435438753
x20 = -71.8078320820524
x21 = -93.8987137572949
x22 = 52.010811709431
x23 = -75.7472895365539
x24 = 38.0481776934764
x25 = 49.367884556411
x26 = 71.8078320820524
x27 = -53.8558740615393
x28 = -49.9164166070378
x29 = -19.7471538225644
x30 = -99.6333670138477
x31 = 84.1248699461267
x32 = -61.7846555205993
x33 = 24.2351433276927
x34 = 58.2939970166106
x35 = 79.9360797413403
x36 = 8.02851455917392
x37 = -29.6705972839036
x38 = -5.93411945678072
x39 = 100.181899064475
x40 = 70.0126362800011
x41 = -45.7276264022514
x42 = -24.0855436775217
x43 = 12.2173047639603
x44 = -42.2369678982628
x45 = -70.0126362800011
x46 = 40.1425727958696
x47 = 78.091017389232
x48 = 93.8987137572949
x49 = -55.6510698635906
x50 = 19.8967534727354
x51 = -86.2192650485199
x52 = -31.7649923862968
x53 = 22.4399475256414
x54 = 5.93411945678072
x55 = -63.7294509728215
x56 = -77.8416846389471
x57 = -21.5423496246157
x58 = 17.9519580205131
x59 = 56.1996019142174
x60 = 82.0304748437335
x61 = 74.3510261349584
x62 = 95.9931088596881
x63 = 44.331363000656
x64 = 76.2958215871807
x65 = 86.2192650485199
x66 = -83.4766047953859
x67 = -87.6155284501153
x68 = -33.85938748869
x69 = -168.598805742652
x70 = -52.010811709431
x71 = 10.1229096615671
x72 = 60.1390593687189
x73 = 111.302139727181
x74 = 54.1052068118242
x75 = -95.9931088596881
x76 = 91.5549859046168
x77 = 14.3116998663535
x78 = -89.7597901025655
x79 = -68.0678408277789
x80 = -8.02851455917392
x81 = 34.1087202389749
x82 = -97.8381712117964
x83 = 66.4222446758985
x84 = 27.8255349317953
x85 = 88.3136601509131
x86 = 32.3135244369236
x87 = 16.1567622184618
x88 = 29.6705972839036
x89 = -73.6528944341607
x90 = -16.1567622184618
x91 = -27.8255349317953
x92 = -60.1390593687189
x93 = -82.0304748437335
x94 = -35.9537825910832
x95 = -47.8220215046446
x96 = -77.1435529381494
x97 = -24.2351433276927
x98 = 42.2369678982628
x99 = -38.0481776934764
x99 = -38.0481776934764
    © Sr Examen – Калькулятор