cos(3*x)=cos(15*x) (уравнение)

Найду корень уравнения: cos(3*x)=cos(15*x)

Вы ввели

cos(3*x) = cos(15*x)

$$\cos{\left (3 x \right )} = \cos{\left (15 x \right )}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

           / 9 ____\
x3 = -I*log\-\/ -1 /

$$x_{3} = - i \log{\left (- \sqrt[9]{-1} \right )}$$

           /     2/9\
x4 = -I*log\-(-1)   /

$$x_{4} = - i \log{\left (- \left(-1\right)^{\frac{2}{9}} \right )}$$

           /    7/9\
x5 = -I*log\(-1)   /

$$x_{5} = - i \log{\left (\left(-1\right)^{\frac{7}{9}} \right )}$$

           /    8/9\
x6 = -I*log\(-1)   /

$$x_{6} = - i \log{\left (\left(-1\right)^{\frac{8}{9}} \right )}$$

           /          ___\
           |  1   I*\/ 3 |
x7 = -I*log|- - - -------|
           \  2      2   /

$$x_{7} = - i \log{\left (- \frac{1}{2} - \frac{\sqrt{3} i}{2} \right )}$$

           /          ___\
           |  1   I*\/ 3 |
x8 = -I*log|- - + -------|
           \  2      2   /

$$x_{8} = - i \log{\left (- \frac{1}{2} + \frac{\sqrt{3} i}{2} \right )}$$

           /        ___\
           |1   I*\/ 3 |
x9 = -I*log|- - -------|
           \2      2   /

$$x_{9} = - i \log{\left (\frac{1}{2} - \frac{\sqrt{3} i}{2} \right )}$$

            /        ___\
            |1   I*\/ 3 |
x10 = -I*log|- + -------|
            \2      2   /

$$x_{10} = - i \log{\left (\frac{1}{2} + \frac{\sqrt{3} i}{2} \right )}$$

                                                   /   /pi\\
                 /    _____________________\       |cos|--||
                 |   /    2/pi\      2/pi\ |       |   \18/|
x11 = -pi - I*log|  /  cos |--| + sin |--| | + atan|-------|
                 \\/       \18/       \18/ /       |   /pi\|
                                                   |sin|--||
                                                   \   \18//

$$x_{11} = - \pi + \operatorname{atan}{\left (\frac{\cos{\left (\frac{\pi}{18} \right )}}{\sin{\left (\frac{\pi}{18} \right )}} \right )} - i \log{\left (\sqrt{\sin^{2}{\left (\frac{\pi}{18} \right )} + \cos^{2}{\left (\frac{\pi}{18} \right )}} \right )}$$

               /   /pi\\                                   
               |cos|--||        /    _____________________\
               |   \18/|        |   /    2/pi\      2/pi\ |
x12 = pi - atan|-------| - I*log|  /  cos |--| + sin |--| |
               |   /pi\|        \\/       \18/       \18/ /
               |sin|--||                                   
               \   \18//                                   

$$x_{12} = - \operatorname{atan}{\left (\frac{\cos{\left (\frac{\pi}{18} \right )}}{\sin{\left (\frac{\pi}{18} \right )}} \right )} + \pi - i \log{\left (\sqrt{\sin^{2}{\left (\frac{\pi}{18} \right )} + \cos^{2}{\left (\frac{\pi}{18} \right )}} \right )}$$

            /   /pi\\                                   
            |cos|--||        /    _____________________\
            |   \18/|        |   /    2/pi\      2/pi\ |
x13 = - atan|-------| - I*log|  /  cos |--| + sin |--| |
            |   /pi\|        \\/       \18/       \18/ /
            |sin|--||                                   
            \   \18//                                   

$$x_{13} = - \operatorname{atan}{\left (\frac{\cos{\left (\frac{\pi}{18} \right )}}{\sin{\left (\frac{\pi}{18} \right )}} \right )} - i \log{\left (\sqrt{\sin^{2}{\left (\frac{\pi}{18} \right )} + \cos^{2}{\left (\frac{\pi}{18} \right )}} \right )}$$

                                               /   /pi\\
             /    _____________________\       |cos|--||
             |   /    2/pi\      2/pi\ |       |   \18/|
x14 = - I*log|  /  cos |--| + sin |--| | + atan|-------|
             \\/       \18/       \18/ /       |   /pi\|
                                               |sin|--||
                                               \   \18//

$$x_{14} = \operatorname{atan}{\left (\frac{\cos{\left (\frac{\pi}{18} \right )}}{\sin{\left (\frac{\pi}{18} \right )}} \right )} - i \log{\left (\sqrt{\sin^{2}{\left (\frac{\pi}{18} \right )} + \cos^{2}{\left (\frac{\pi}{18} \right )}} \right )}$$

            / -2*pi*I\
            | -------|
            |    9   |
x15 = -I*log\e       /

$$x_{15} = - i \log{\left (e^{- \frac{2 \pi}{9} i} \right )}$$

            / -pi*I \
            | ------|
            |   9   |
x16 = -I*log\e      /

$$x_{16} = - i \log{\left (e^{- \frac{i \pi}{9}} \right )}$$

            / pi*I\
            | ----|
            |  9  |
x17 = -I*log\e    /

$$x_{17} = - i \log{\left (e^{\frac{i \pi}{9}} \right )}$$

            / 2*pi*I\
            | ------|
            |   9   |
x18 = -I*log\e      /

$$x_{18} = - i \log{\left (e^{\frac{2 \pi}{9} i} \right )}$$

Численный ответ

x1 = -100.007366139000

x2 = 21.9911485832000

x3 = -503.003890425000

x4 = -23.7364778271000

x5 = 95.9931088597000

x6 = -1.74532925199000

x7 = -51.8362787842000

x8 = -75.7472895366000

x9 = -39.7935069061000

x10 = -74.0019602846000

x11 = 36.1283155163000

x12 = -71.7330322570000

x13 = 48.1710873782000

x14 = 23.5619449019000

x15 = 14.1371669412000

x16 = 28.2743338721000

x17 = 32.1140582367000

x18 = -5.75958653158000

x19 = -15.7079632410000

x20 = -7.85398163397000

x21 = -53.7561409614000

x22 = -42.2369678983000

x23 = 38.2227106187000

x24 = 89.3608577021000

x25 = -17.8023583241000

x26 = -95.6440430093000

x27 = 26.1799388284000

x28 = -27.7507351067000

x29 = -65.9734457811000

x30 = 87.9645943009000

x31 = 38.3972435439000

x32 = -79.9360797413000

x33 = -31.7649923863000

x34 = 65.9734457354000

x35 = -43.9822971825000

x36 = 92.5024503557000

x37 = 43.9822971616000

x38 = -11.8682389136000

x39 = -70.1622359874000

x40 = -25.8308729295000

x41 = -3.83972435439000

x42 = -33.1612557879000

x43 = 84.4739357965000

x44 = 6.28318530287000

x45 = 0.0

x46 = 16.2315620435000

x47 = -57.9449311662000

x48 = -13.9626340160000

x49 = 86.3937979737000

x50 = -87.9645943788000

x51 = -49.7418836818000

x52 = 78.8888821901000

x53 = -93.7241808321000

x54 = 52.0108117094000

x55 = -35.9537825911000

x56 = 74.0019602846000

x57 = 34.2084533391000

x58 = -83.7758040730000

x59 = -61.7846554894000

x60 = 55.8505360638000

x61 = -45.5530934771000

x62 = 54.1052068118000

x63 = 50.2654824485000

x64 = 86.2192650485000

x65 = 76.0963553870000

x66 = 20.2458193231000

x67 = 10.1229096616000

x68 = 60.3883921190000

x69 = -47.8220215046000

x70 = -91.8043186549000

x71 = -88.6627260013000

x72 = -29.8451302091000

x73 = -33.8593874887000

x74 = -78.0162175641000

x75 = 94.2477796094000

x76 = 1.74532925199000

x77 = 63.8790505605000

x78 = 18.1514242207000

x79 = -8.90117918517000

x80 = 58.1194640914000

x81 = -97.7384381117000

x82 = -69.8131700798000

x83 = 98.0875039621000

x84 = 4.18879025535000

x85 = 42.2369678983000

x86 = 64.2281164734000

x87 = 10.4719754616000

x88 = -65.2753140246000

x89 = 72.2566310280000

x90 = -20.4203522483000

x91 = 8.02851455917000

x92 = 70.6858347058000

x93 = -21.9911485885000

График