sin(x)=-1/2 (уравнение)

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

    Решение

    Вы ввели
    [LaTeX]
    sin(x) = -1/2
    $$\sin{\left (x \right )} = - \frac{1}{2}$$
    Подробное решение
    [LaTeX]
    Дано уравнение
    $$\sin{\left (x \right )} = - \frac{1}{2}$$
    - это простейшее тригонометрическое ур-ние
    Это ур-ние преобразуется в
    $$x = 2 \pi n + \operatorname{asin}{\left (- \frac{1}{2} \right )}$$
    $$x = 2 \pi n - \operatorname{asin}{\left (- \frac{1}{2} \right )} + \pi$$
    Или
    $$x = 2 \pi n - \frac{\pi}{6}$$
    $$x = 2 \pi n + \frac{7 \pi}{6}$$
    , где n - любое целое число
    График
    [LaTeX]
    Быстрый ответ
    [LaTeX]
         -pi 
    x1 = ----
          6  
    $$x_{1} = - \frac{\pi}{6}$$
         7*pi
    x2 = ----
          6  
    $$x_{2} = \frac{7 \pi}{6}$$
    Численный ответ
    [LaTeX]
    x1 = -69.6386371546000
    x2 = -88.4881930761000
    x3 = -38.2227106187000
    x4 = 100.007366139000
    x5 = -52.8834763354000
    x6 = -78.0162175641000
    x7 = -15.1843644924000
    x8 = 37.1755130675000
    x9 = 41.3643032723000
    x10 = 437.204977625000
    x11 = 72.7802298082000
    x12 = -40.3171057211000
    x13 = 9.94837673637000
    x14 = 62.3082542962000
    x15 = 12.0427718388000
    x16 = -21.4675497995000
    x17 = -8.90117918517000
    x18 = 49.7418836818000
    x19 = -90.5825881785000
    x20 = -46.6002910282000
    x21 = -71.7330322570000
    x22 = 192.160750645000
    x23 = 47.6474885794000
    x24 = 87.4409955249000
    x25 = -63.3554518474000
    x26 = -44.5058959259000
    x27 = -94.7713783833000
    x28 = -195.302343298000
    x29 = -27.7507351067000
    x30 = 68.5914396034000
    x31 = 93.7241808321000
    x32 = 5.75958653158000
    x33 = -50.7890812330000
    x34 = -65.4498469498000
    x35 = 43.4586983747000
    x36 = -0.523598775598000
    x37 = -96.8657734857000
    x38 = 66.4970445010000
    x39 = 22.5147473507000
    x40 = -82.2050077689000
    x41 = -84.2994028713000
    x42 = 30.8923277603000
    x43 = 18.3259571459000
    x44 = 79.0634151153000
    x45 = -57.0722665402000
    x46 = -13.0899693900000
    x47 = 85.3466004225000
    x48 = -34.0339204139000
    x49 = 81.1578102177000
    x50 = -101.054563690000
    x51 = 53.9306738866000
    x52 = 56.0250689890000
    x53 = -151.320046148000
    x54 = 35.0811179651000
    x55 = -2.61799387799000
    x56 = 3.66519142919000
    x57 = 24.6091424531000
    x58 = 28.7979326579000
    x59 = -6.80678408278000
    x60 = 97.9129710369000
    x61 = 74.8746249106000
    x62 = -59.1666616426000
    x63 = 60.2138591938000
    x64 = -19.3731546971000
    x65 = 91.6297857297000
    x66 = -31.9395253115000
    x67 = -25.6563400043000
    x68 = 66400.1787275000
    x69 = 16.2315620435000
    x70 = -75.9218224618000