sin(x)=-12/13 (уравнение)

Найду корень уравнения: sin(x)=-12/13

Вы ввели

         -12 
sin(x) = ----
          13 

$$\sin{\left(x \right)} = - \frac{12}{13}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{12}{13}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{12}{13} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{12}{13} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{12}{13} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{12}{13} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

              /12\
x1 = pi + asin|--|
              \13/

$$x_{1} = \operatorname{asin}{\left(\frac{12}{13} \right)} + \pi$$

          /12\
x2 = -asin|--|
          \13/

$$x_{2} = - \operatorname{asin}{\left(\frac{12}{13} \right)}$$

Сумма и произведение корней

сумма

             /12\       /12\
0 + pi + asin|--| - asin|--|
             \13/       \13/

$$- \operatorname{asin}{\left(\frac{12}{13} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{12}{13} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

  /         /12\\      /12\
1*|pi + asin|--||*-asin|--|
  \         \13//      \13/

$$1 \left(\operatorname{asin}{\left(\frac{12}{13} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{12}{13} \right)}\right)$$

=

 /         /12\\     /12\
-|pi + asin|--||*asin|--|
 \         \13//     \13/

$$- \left(\operatorname{asin}{\left(\frac{12}{13} \right)} + \pi\right) \operatorname{asin}{\left(\frac{12}{13} \right)}$$

Численный ответ

x1 = -64.007858278891

x2 = -114.273340736328

x3 = 49.0894772503416

x4 = -71.0806258254701

x5 = -77.3638111326497

x6 = 23.9567360216232

x7 = -26.3087464358135

x8 = -96.2133670541885

x9 = 36.5231066359824

x10 = 79.71582154684

x11 = 16.8839684750441

x12 = -82.8574142004298

x13 = 74.2222184790599

x14 = 60.8662656253012

x15 = -58.5142552111109

x16 = -70.2910435860706

x17 = 85.9990068540196

x18 = 98.5653774683787

x19 = -64.7974405182905

x20 = 61.6558478647007

x21 = -14.5319580608538

x22 = 11.390365407264

x23 = -1.96558744649466

x24 = 17.6735507144436

x25 = 67.9390331718803

x26 = 30.2399213288028

x27 = -89.9301817470089

x28 = -45.9478845967518

x29 = 10.6007831678645

x30 = -13.7423758214543

x31 = 4.31759786068493

x32 = 92.2821921611991

x33 = 42.806291943162

x34 = 54.5830803181216

x35 = 29.4503390894033

x36 = -33.3815139823926

x37 = -8.24877275367425

x38 = -76.5742288932502

x39 = 99.3549597077782

x40 = 5.10718010008445

x41 = -89.1405995076094

x42 = 73.4326362396604

x43 = -7.45919051427472

x44 = 86.7885890934191

x45 = -1.17600520709514

x46 = -27.098328675213

x47 = 282924.375191782

x48 = 48.299895010942

x49 = 67.1494509324808

x50 = -83.6469964398293

x51 = -51.4414876645318

x52 = 23.1671537822237

x53 = -101.706970121969

x54 = -38.8751170501727

x55 = 42.0167097037624

x56 = -57.7246729717114

x57 = -95.4237848147889

x58 = 55.3726625575211

x59 = 431.574198748897

x60 = -742.591871454286

x61 = -32.5919317429931

x62 = -39.6646992895722

x63 = 80.5054037862395

x64 = 35.7335243965829

x65 = 93.0717744005987

x66 = -45.1583023573522

x67 = -20.8151433680334

x68 = -20.0255611286339

x69 = -52.2310699039313

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