sin(2*x)=-1 (уравнение)

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    Найду корень уравнения: sin(2*x)=-1

    Решение

    Вы ввели
    [LaTeX]
    sin(2*x) = -1
    $$\sin{\left (2 x \right )} = -1$$
    Подробное решение
    [LaTeX]
    Дано уравнение
    $$\sin{\left (2 x \right )} = -1$$
    - это простейшее тригонометрическое ур-ние
    Это ур-ние преобразуется в
    $$2 x = 2 \pi n + \operatorname{asin}{\left (-1 \right )}$$
    $$2 x = 2 \pi n - \operatorname{asin}{\left (-1 \right )} + \pi$$
    Или
    $$2 x = 2 \pi n - \frac{\pi}{2}$$
    $$2 x = 2 \pi n + \frac{3 \pi}{2}$$
    , где n - любое целое число
    Разделим обе части полученного ур-ния на
    $$2$$
    получим ответ:
    $$x_{1} = \pi n - \frac{\pi}{4}$$
    $$x_{2} = \pi n + \frac{3 \pi}{4}$$
    График
    [LaTeX]
    Быстрый ответ
    [LaTeX]
         -pi 
    x1 = ----
          4  
    $$x_{1} = - \frac{\pi}{4}$$
         3*pi
    x2 = ----
          4  
    $$x_{2} = \frac{3 \pi}{4}$$
    Численный ответ
    [LaTeX]
    x1 = 43.1968992295000
    x2 = 87.1791959596000
    x3 = -38.4845097737000
    x4 = -38.4845103584000
    x5 = -54.1924731446000
    x6 = 43.1968988259000
    x7 = -73.0420291966000
    x8 = 18.0641575838000
    x9 = -51.0508808708000
    x10 = -7.06858372020000
    x11 = 52.6216767646000
    x12 = 90.3207887448000
    x13 = -7.06858355299000
    x14 = -0.785398304611000
    x15 = 96.6039739773000
    x16 = -76.1836225361000
    x17 = -91.8915845717000
    x18 = 80.8960105952000
    x19 = -35.3429175479000
    x20 = -95.0331780209000
    x21 = -88.7499925538000
    x22 = -60.4756585175000
    x23 = -98.1747703034000
    x24 = 80.8960105825000
    x25 = 74.6128253429000
    x26 = -96953.4762811000
    x27 = 24.3473430044000
    x28 = -10.2101759861000
    x29 = 58.9048620636000
    x30 = -51.0508806462000
    x31 = 14.9225648553000
    x32 = 49.4800845343000
    x33 = 36.9137135282000
    x34 = -35.3429178934000
    x35 = 11.7809725931000
    x36 = -60.4756583509000
    x37 = -63.6172513150000
    x38 = 65.1880478022000
    x39 = 77.7544183301000
    x40 = -13.3517689699000
    x41 = 30.6305281864000
    x42 = 21.2057502602000
    x43 = 14.9225649892000
    x44 = 55.7632697512000
    x45 = -0.785397916652000
    x46 = 65.1880473924000
    x47 = -32.2013245653000
    x48 = -3.92699107594000
    x49 = 21.2057506565000
    x50 = -82.4668069282000
    x51 = 40.0553062100000
    x52 = 58.9048620067000
    x53 = -66.7588436373000
    x54 = -66.7588439932000
    x55 = 96.6039739212000
    x56 = -22.7765468685000
    x57 = 36.9137134309000
    x58 = 62.0464547256000
    x59 = -79.3252147038000
    x60 = -44.7676954314000
    x61 = -101.316363786000
    x62 = 5.49778738042000
    x63 = -22.7765464900000
    x64 = 87.1791963747000
    x65 = 93.4623816879000
    x66 = -76.1836217239000
    x67 = 71.4712331111000
    x68 = 99.7455669090000
    x69 = 46.3384915844000
    x70 = 33.7721211722000
    x71 = 62.0464548196000
    x72 = -29.0597322956000
    x73 = 68.3296401645000
    x74 = -73.0420294459000
    x75 = 84.0376034200000
    x76 = 27.4889359574000
    x77 = -85.6083998947000
    x78 = -88.7499922112000
    x79 = -29.0597320982000
    x80 = 55.7632697006000
    x81 = -95.0331777492000
    x82 = -41.6261027353000
    x83 = -44.7676950636000
    x84 = -19.6349541555000
    x85 = 8.63937960823000
    x86 = -57.3340661259000
    x87 = 2.35619442441000
    x88 = -16.4933611966000