2*sin(x)-1=0 (уравнение)

Найду корень уравнения: 2*sin(x)-1=0

Вы ввели

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2*sin(x) - 1 = 0

$$2 \sin{\left (x \right )} - 1 = 0$$

Подробное решение

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Дано уравнение
$$2 \sin{\left (x \right )} - 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$2 \sin{\left (x \right )} = 1$$

Разделим обе части ур-ния на 2

Ур-ние превратится в
$$\sin{\left (x \right )} = \frac{1}{2}$$
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
$$x = 2 \pi n + \frac{\pi}{6}$$
$$x = 2 \pi n + \frac{5 \pi}{6}$$
, где n - любое целое число

Быстрый ответ

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     pi
x1 = --
     6 

$$x_{1} = \frac{\pi}{6}$$

     5*pi
x2 = ----
      6  

$$x_{2} = \frac{5 \pi}{6}$$

Численный ответ

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[text]

x1 = -35.0811179651000

x2 = -81.1578102177000

x3 = -30.8923277603000

x4 = -66.4970445010000

x5 = 17438.4572213000

x6 = -28.7979326579000

x7 = 2.61799387799000

x8 = -91.6297857297000

x9 = 71.7330322570000

x10 = 138.753675534000

x11 = 6.80678408278000

x12 = 84.2994028713000

x13 = 19.3731546971000

x14 = 69.6386371546000

x15 = 88.4881930761000

x16 = 59.1666616426000

x17 = -93.7241808321000

x18 = -22.5147473507000

x19 = 46.6002910282000

x20 = -49.7418836818000

x21 = -24.6091424531000

x22 = 38.2227106187000

x23 = -60.2138591938000

x24 = 90.5825881785000

x25 = 44.5058959259000

x26 = -43.4586983747000

x27 = 40.3171057211000

x28 = 94.7713783833000

x29 = -85.3466004225000

x30 = 134.564885329000

x31 = -79.0634151153000

x32 = 34.0339204139000

x33 = -87.4409955249000

x34 = 101.054563690000

x35 = -74.8746249106000

x36 = 21.4675497995000

x37 = -12.0427718388000

x38 = 52.8834763354000

x39 = 50.7890812330000

x40 = -68.5914396034000

x41 = -62.3082542962000

x42 = -100.007366139000

x43 = -627.794931942000

x44 = -41.3643032723000

x45 = 13.0899693900000

x46 = 31.9395253115000

x47 = -56.0250689890000

x48 = -18.3259571459000

x49 = 75.9218224618000

x50 = -3.66519142919000

x51 = -2650.98060085000

x52 = -16.2315620435000

x53 = 25.6563400043000

x54 = -5.75958653158000

x55 = 63.3554518474000

x56 = 15.1843644924000

x57 = 57.0722665402000

x58 = -97.9129710369000

x59 = -53.9306738866000

x60 = 0.523598775598000

x61 = -37.1755130675000

x62 = 78.0162175641000

x63 = 65.4498469498000

x64 = -72.7802298082000

x65 = 27.7507351067000

x66 = 8.90117918517000

x67 = -47.6474885794000

x68 = -4454.25478401000

x69 = 96.8657734857000

x70 = -9.94837673637000

x71 = 82.2050077689000