sin(x)=-5/13 (уравнение)

Найду корень уравнения: sin(x)=-5/13

Вы ввели

sin(x) = -5/13

$$\sin{\left(x \right)} = - \frac{5}{13}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{5}{13}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{5}{13} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{5}{13} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{5}{13} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{5}{13} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(5/13)

$$x_{1} = \operatorname{asin}{\left(\frac{5}{13} \right)} + \pi$$

x2 = -asin(5/13)

$$x_{2} = - \operatorname{asin}{\left(\frac{5}{13} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(5/13) - asin(5/13)

$$- \operatorname{asin}{\left(\frac{5}{13} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{5}{13} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi + asin(5/13))*-asin(5/13)

$$1 \left(\operatorname{asin}{\left(\frac{5}{13} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{5}{13} \right)}\right)$$

=

-(pi + asin(5/13))*asin(5/13)

$$- \left(\operatorname{asin}{\left(\frac{5}{13} \right)} + \pi\right) \operatorname{asin}{\left(\frac{5}{13} \right)}$$

Численный ответ

x1 = -75.7930148058548

x2 = 41.2354956163671

x3 = 56.1538766449165

x4 = -40.4459133769676

x5 = -90.7113958344042

x6 = -6.67797642687935

x7 = -15.3131721482492

x8 = 68.7202472592757

x9 = 112.702544409533

x10 = -50.6602735771365

x11 = 28.6691250020079

x12 = -21.5963574554288

x13 = 5.88839418747983

x14 = 49.8706913377369

x15 = -96.9945811415838

x16 = -25.5275323484181

x17 = 31.0211354161982

x18 = -59.2954692985063

x19 = -34.162728069788

x20 = -71.8618399128655

x21 = 12.1715794946594

x22 = 43.5875060305573

x23 = 66.3682368450854

x24 = -316.906066892869

x25 = -84.4282105272246

x26 = -295.70450055714

x27 = -103.277766448763

x28 = -94.6425707273936

x29 = -12.9611617340589

x30 = 91.5009780738038

x31 = 37.3043207233778

x32 = 16.1027543876487

x33 = -88.359385420214

x34 = 34.9523103091875

x35 = 3.53638377328955

x36 = 93.852988487994

x37 = -44.3770882699569

x38 = -69.5098294986752

x39 = -82.0762001130344

x40 = 18.454764801839

x41 = 47.5186809235467

x42 = 78.9346074594446

x43 = 97.7841633809834

x44 = -100.925756034573

x45 = -2.74680153389003

x46 = -9.02998684106962

x47 = 85.2177927666242

x48 = 100.136173795174

x49 = 22.3859396948283

x50 = 81.2866178736349

x51 = -0.394791119699761

x52 = -78.1450252200451

x53 = -38.0939029627773

x54 = -31.8107176555977

x55 = 9.81956908046914

x56 = -56.943458884316

x57 = 87.5698031808144

x58 = 62.4370619520961

x59 = 72.651422152265

x60 = -53.0122839913267

x61 = -46.7290986841471

x62 = -27.8795427626084

x63 = -65.5786546056859

x64 = 60.0850515379058

x65 = -19.2443470412385

x66 = 24.7379501090186

x67 = -2595.35032298487

x68 = 75.0034325664553

x69 = 53.8018662307262

x70 = -63.2266441914956

x71 = 4523.4986300496

x72 = 307.4812889321

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