Решение уравнений/ Любые/ sin(x/2)=cos(x/3)

sin(x/2)=cos(x/3) (уравнение)

Учитель очень удивится увидев твоё верное решение 😼

Примеры
Неизвестное в уравнении :

Искать численное решение на промежутке:

[, ]

    Найду корень уравнения: sin(x/2)=cos(x/3)

    Решение

    Вы ввели [src]
       /x\      /x\
sin|-| = cos|-|
   \2/      \3/
    sin⁡(x2)=cos⁡(x3)\sin{\left(\frac{x}{2} \right)} = \cos{\left(\frac{x}{3} \right)}
    Упростить
    График
    0-80-60-40-2020406080-1001002-2
    Построить график f1(x)
    Построить график f2(x)
    Сумма и произведение корней [src]
    сумма
                         /                         ___________             ___________\          /               ___________             ___________             ___________                      ___________\          /                         ___________            ___________             ___________             ___________\
                     |          ___     ___   /       ___      ____   /       ___ |          |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |          |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |
3*pi                 |  I   I*\/ 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  |
---- + 3*pi - 6*I*log|- - - ------- - -------------------- + ---------------------| - 6*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------| - 6*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
 5                   \  4      4               8                       8          /          \  4            16                      16                      16               4               16         /          \  4      4               16                     16                      16                      16         /
    −6ilog⁡(−105+516−25+516−25−516+105−516−5i4−i4)+((−6ilog⁡(−25+58+105+58−5i4−i4)+(3π5+3π))−6ilog⁡(−105+516−105−516−25+516+25−516−i4+5i4))- 6 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(- 6 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(\frac{3 \pi}{5} + 3 \pi\right)\right) - 6 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)
    =
                   /                         ___________             ___________\          /                         ___________            ___________             ___________             ___________\          /               ___________             ___________             ___________                      ___________\
               |          ___     ___   /       ___      ____   /       ___ |          |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |          |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |
18*pi          |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  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  |
----- - 6*I*log|- - - ------- - -------------------- + ---------------------| - 6*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------| - 6*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
  5            \  4      4               8                       8          /          \  4      4               16                     16                      16                      16         /          \  4            16                      16                      16               4               16         /
    −6ilog⁡(−105+516−25+516−25−516+105−516−5i4−i4)−6ilog⁡(−25+58+105+58−5i4−i4)+18π5−6ilog⁡(−105+516−105−516−25+516+25−516−i4+5i4)- 6 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)} - 6 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)} + \frac{18 \pi}{5} - 6 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)}
    произведение
                      /                         ___________             ___________\         /               ___________             ___________             ___________                      ___________\         /                         ___________            ___________             ___________             ___________\
                  |          ___     ___   /       ___      ____   /       ___ |         |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |         |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |
3*pi              |  I   I*\/ 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  |
----*3*pi*-6*I*log|- - - ------- - -------------------- + ---------------------|*-6*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|*-6*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
 5                \  4      4               8                       8          /         \  4            16                      16                      16               4               16         /         \  4      4               16                     16                      16                      16         /
    −6ilog⁡(−105+516−25+516−25−516+105−516−5i4−i4)−6ilog⁡(−105+516−105−516−25+516+25−516−i4+5i4)−6ilog⁡(−25+58+105+58−5i4−i4)3π5⋅3π- 6 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)} - 6 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)} - 6 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)} \frac{3 \pi}{5} \cdot 3 \pi
    =
                  /                         ___________             ___________\    /                         ___________            ___________             ___________             ___________\    /               ___________             ___________             ___________                      ___________\
              |          ___     ___   /       ___      ____   /       ___ |    |          ___     ___   /       ___      ___   /       ___      ____   /       ___      ____   /       ___ |    |        ___   /       ___      ____   /       ___      ____   /       ___        ___     ___   /       ___ |
         2    |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  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  |
1944*I*pi *log|- - - ------- - -------------------- + ---------------------|*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
              \  4      4               8                       8          /    \  4      4               16                     16                      16                      16         /    \  4            16                      16                      16               4               16         /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                      5
    1944iπ2log⁡(−25+58+105+58−5i4−i4)log⁡(−105+516−105−516−25+516+25−516−i4+5i4)log⁡(−105+516−25+516−25−516+105−516−5i4−i4)5\frac{1944 i \pi^{2} \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)} \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)} \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)}}{5}
    Быстрый ответ [src]
         3*pi
x1 = ----
      5
    x1=3π5x_{1} = \frac{3 \pi}{5}
    x2 = 3*pi
    x2=3πx_{2} = 3 \pi
                 /                         ___________             ___________\
             |          ___     ___   /       ___      ____   /       ___ |
             |  I   I*\/ 5    \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5  |
x3 = -6*I*log|- - - ------- - -------------------- + ---------------------|
             \  4      4               8                       8          /
    x3=−6ilog⁡(−25+58+105+58−5i4−i4)x_{3} = - 6 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   \/ 2 *\/  5 + \/ 5     \/ 10 *\/  5 + \/ 5     \/ 10 *\/  5 - \/ 5     I*\/ 5    \/ 2 *\/  5 - \/ 5  |
x4 = -6*I*log|- - - -------------------- - --------------------- - --------------------- + ------- + --------------------|
             \  4            16                      16                      16               4               16         /
    x4=−6ilog⁡(−105+516−105−516−25+516+25−516−i4+5i4)x_{4} = - 6 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  |
x5 = -6*I*log|- - - ------- - -------------------- - -------------------- - --------------------- + ---------------------|
             \  4      4               16                     16                      16                      16         /
    x5=−6ilog⁡(−105+516−25+516−25−516+105−516−5i4−i4)x_{5} = - 6 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)}
    Численный ответ [src]
    x1 = -50.8938009881547
    x2 = -88.5929128312322
    x3 = -28.2743345278988
    x4 = 47.1238890106496
    x5 = -96.1327351998477
    x6 = -28.2743341667712
    x7 = 16.9646003293849
    x8 = -65.9734449664942
    x9 = 32.0442450666159
    x10 = 84.8230022978442
    x11 = 9.4247776746118
    x12 = 54.6637121724624
    x13 = 84.8230022103226
    x14 = 84.8230013544733
    x15 = 47.1238914557766
    x16 = 1411.83173852325
    x17 = 24.5044226980004
    x18 = -65.9734464582615
    x19 = -5.65486677646163
    x20 = -28.2743337049001
    x21 = -20.7345115136926
    x22 = -65.9734457649087
    x23 = -13.1946891450771
    x24 = 9.42477880342571
    x25 = 47.1238882143797
    x26 = 92.3628240155399
    x27 = -2177.12371038668
    x28 = 499.513233005087
    x29 = 1.88495559215388
    x30 = -58.4336233567702
    x31 = -65.973447783358
    x32 = 69.7433569096934
    x33 = -73.5132680940012
    x34 = 99.9026463841554
    x35 = -65.9734449331859
    x36 = 47.1238902506659
    x37 = -171.530958886003
    x38 = 84.8230018402765
    x39 = -35.8141562509236
    x40 = 9.42477827907526
    x41 = 47.1238905994607
    x42 = 84.8230008105818
    x43 = -28.2743330468393
    x44 = 39.5840674352314
    x45 = -43.3539786195391
    x46 = 47.123889381652
    x47 = 77.2831792783089
    x48 = -81.0530904626167
    x49 = 9.4247773089501
    x50 = 62.2035345410779
    x51 = 9.42477741995127
    x52 = -103.672557831161
    График
    sin(x/2)=cos(x/3) (уравнение) /media/krcore-image-pods/hash/equation/6/74/4100024f1038544c0055a9159c70c.png