sin(x)=(2/125) (уравнение)

Найду корень уравнения: sin(x)=(2/125)

Вы ввели

sin(x) = 2/125

$$\sin{\left(x \right)} = \frac{2}{125}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{2}{125}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{125} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{125} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{2}{125} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{2}{125} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(2/125)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{2}{125} \right)}$$

x2 = asin(2/125)

$$x_{2} = \operatorname{asin}{\left(\frac{2}{125} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(2/125) + asin(2/125)

$$\operatorname{asin}{\left(\frac{2}{125} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{2}{125} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(2/125))*asin(2/125)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{2}{125} \right)}\right) \operatorname{asin}{\left(\frac{2}{125} \right)}$$

=

(pi - asin(2/125))*asin(2/125)

$$\left(\pi - \operatorname{asin}{\left(\frac{2}{125} \right)}\right) \operatorname{asin}{\left(\frac{2}{125} \right)}$$

Численный ответ

x1 = 91.0901862713587

x2 = 3.12559197084447

x3 = 43.9982978330024

x4 = -65.989446408131

x5 = -15.7239639506943

x6 = 87.9805949832595

x7 = 6.29918598992491

x8 = 15.6919625852036

x9 = -75.3822230034097

x10 = -87.9485936177689

x11 = -12.5503699316139

x12 = 12.5823712971045

x13 = 21.9751478923832

x14 = 75.4142243689004

x15 = -50.2494817746914

x16 = -22.0071492578739

x17 = 50.281483140182

x18 = 53.3910744282812

x19 = 9.40877727802406

x20 = -144.497261382385

x21 = 1143.55572658943

x22 = 97.3733715785383

x23 = 100.546965597619

x24 = 69.1310390617208

x25 = -59.7062611009514

x26 = -9.4407786435147

x27 = -34.573519872233

x28 = 31.4319272186433

x29 = -25.116740545973

x30 = 56.5646684473616

x31 = -43.9662964675118

x32 = -6.26718462443426

x33 = -28.2903345650535

x34 = 37.7151125258228

x35 = 40.824703813922

x36 = -69.0990376962301

x37 = -40.8567051794126

x38 = 207.361115819672

x39 = 72.2406303498199

x40 = 78.5238156569995

x41 = -84.8390023296697

x42 = -31.3999258531526

x43 = -72.2726317153106

x44 = -94.2317789249485

x45 = 47.1078891211016

x46 = 28.2583331995628

x47 = -3.15759333633512

x48 = 62.8478537545412

x49 = -18.8335552387934

x50 = 94.2637802904391

x51 = -53.4230757937718

x52 = -78.5558170224901

x53 = -37.6831111603322

x54 = -100.514964232128

x55 = 562.329084309828

x56 = -91.1221876368493

x57 = 65.9574450426403

x58 = -97.4053729440289

x59 = 34.5415185067424

x60 = -103.688558251209

x61 = -47.1398904865922

x62 = 18.8655566042841

x63 = 25.1487419114637

x64 = 81.6974096760799

x65 = 84.8070009641791

x66 = -81.6654083105893

x67 = -62.8158523890505

x68 = 59.6742597354608

x69 = -56.532667081871

x70 = 0.0160006827453219

График