sin(x)=√3/3 (уравнение)

Найду корень уравнения: sin(x)=√3/3

Вы ввели

           ___
         \/ 3 
sin(x) = -----
           3  

$$\sin{\left(x \right)} = \frac{\sqrt{3}}{3}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

              /  ___\
              |\/ 3 |
x1 = pi - asin|-----|
              \  3  /

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$

         /  ___\
         |\/ 3 |
x2 = asin|-----|
         \  3  /

$$x_{2} = \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$

Сумма и произведение корней

сумма

             /  ___\       /  ___\
             |\/ 3 |       |\/ 3 |
0 + pi - asin|-----| + asin|-----|
             \  3  /       \  3  /

$$\operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

  /         /  ___\\     /  ___\
  |         |\/ 3 ||     |\/ 3 |
1*|pi - asin|-----||*asin|-----|
  \         \  3  //     \  3  /

$$1 \left(\pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}\right) \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$

=

/         /  ___\\     /  ___\
|         |\/ 3 ||     |\/ 3 |
|pi - asin|-----||*asin|-----|
\         \  3  //     \  3  /

$$\left(\pi - \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}\right) \operatorname{asin}{\left(\frac{\sqrt{3}}{3} \right)}$$

Численный ответ

x1 = -37.0836321344071

x2 = 84.207521938254

x3 = 101.146444623544

x4 = -3.75707236226018

x5 = -41.4561842053377

x6 = 94.8632593163642

x7 = 63.4473327804663

x8 = -10.0402576694398

x9 = 2.52611294491941

x10 = -62.2163733631255

x11 = 90.4907072454336

x12 = -43.3668174415867

x13 = 76.0137033948254

x14 = 46.5084100951765

x15 = -35.1729988981581

x16 = -79.1552960484152

x17 = 57.1641474732867

x18 = 15.0924835592786

x19 = 69.7305180876458

x20 = 402.739339368164

x21 = 88.5800740091846

x22 = 19.4650356302091

x23 = 27.6588541736378

x24 = 50.8809621661071

x25 = 21.3756688664582

x26 = -47.7393695125173

x27 = -22.6066282837989

x28 = -28.8898135909785

x29 = 0.615479708670387

x30 = -74.7827439774847

x31 = -24.517261520048

x32 = -99.915485206203

x33 = -93.6322998990234

x34 = -98.004851969954

x35 = 52.7915954023561

x36 = 71.6411513238949

x37 = 33.9420394808173

x38 = 38.3145915517479

x39 = 44.5977768589275

x40 = -49.6500027487663

x41 = -66.5889254340561

x42 = -68.4995586703051

x43 = 113.712815237903

x44 = -55.9331880559459

x45 = -87.3491145918438

x46 = -11.9508909056888

x47 = -185.969446270468

x48 = -72.8721107412356

x49 = -85.4384813555948

x50 = 59.0747807095357

x51 = -707.473826766374

x52 = -948.145501675447

x53 = 40.2252247879969

x54 = 32.0314062445683

x55 = -18344.3749840195

x56 = -91.7216666627744

x57 = 96.7738925526132

x58 = -81.0659292846642

x59 = -16.3234429766194

x60 = -5.6677055985092

x61 = 25.7482209373887

x62 = -18.2340762128684

x63 = -60.3057401268765

x64 = 82.296888702005

x65 = 8.80929825209899

x66 = -30.8004468272275

x67 = 13.1818503230296

x68 = 6.89866501584997

x69 = 65.3579660167153

x70 = -571.154383244672

x71 = -54.0225548196969

x72 = -451.77386240826

x73 = 77.9243366310744

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