sinx=-(1/√3) (уравнение)

Найду корень уравнения: sinx=-(1/√3)

Вы ввели

          -1  
sin(x) = -----
           ___
         \/ 3 

$$\sin{\left(x \right)} = - \frac{1}{\sqrt{3}}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{1}{\sqrt{3}}$$
- 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

Сумма и произведение корней

сумма

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

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Быстрый ответ

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

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

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

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

Численный ответ

x1 = 173.403075656109

x2 = 91.7216666627744

x3 = -15.0924835592786

x4 = -52.7915954023561

x5 = 55.9331880559459

x6 = 1142.92424619801

x7 = 99.915485206203

x8 = 3.75707236226018

x9 = -77.9243366310744

x10 = 11.9508909056888

x11 = -101.146444623544

x12 = -82.296888702005

x13 = -2.52611294491941

x14 = 49.6500027487663

x15 = -103.057077859793

x16 = -38.3145915517479

x17 = 5.6677055985092

x18 = -84.207521938254

x19 = -0.615479708670387

x20 = -1049.90742600766

x21 = -8.80929825209899

x22 = 37.0836321344071

x23 = -50.8809621661071

x24 = -27.6588541736378

x25 = -69.7305180876458

x26 = -96.7738925526132

x27 = 79.1552960484152

x28 = -1583.97817711793

x29 = 16.3234429766194

x30 = -9877.78278259498

x31 = -57.1641474732867

x32 = 93.6322998990234

x33 = -59.0747807095357

x34 = -19.4650356302091

x35 = 54.0225548196969

x36 = -32.0314062445683

x37 = -21.3756688664582

x38 = -63.4473327804663

x39 = 85.4384813555948

x40 = -6.89866501584997

x41 = 10.0402576694398

x42 = -119.996000545083

x43 = -90.4907072454336

x44 = -40.2252247879969

x45 = 98.004851969954

x46 = -65.3579660167153

x47 = 30.8004468272275

x48 = 24.517261520048

x49 = 60.3057401268765

x50 = 47.7393695125173

x51 = 22.6066282837989

x52 = -44.5977768589275

x53 = -94.8632593163642

x54 = -88.5800740091846

x55 = 66.5889254340561

x56 = -76.0137033948254

x57 = 68.4995586703051

x58 = 62.2163733631255

x59 = 74.7827439774847

x60 = 28.8898135909785

x61 = -71.6411513238949

x62 = -260.136710539282

x63 = 87.3491145918438

x64 = 81.0659292846642

x65 = -25.7482209373887

x66 = 18.2340762128684

x67 = -46.5084100951765

x68 = -13.1818503230296

x69 = 72.8721107412356

x70 = 35.1729988981581

x71 = 41.4561842053377

x72 = -33.9420394808173

x73 = 43.3668174415867

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