sin(x)=-1/8 (уравнение)

Найду корень уравнения: sin(x)=-1/8

Вы ввели

sin(x) = -1/8

$$\sin{\left(x \right)} = - \frac{1}{8}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = - \frac{1}{8}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{8} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{8} \right)} + \pi$$
Или
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{8} \right)}$$
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{8} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi + asin(1/8)

$$x_{1} = \operatorname{asin}{\left(\frac{1}{8} \right)} + \pi$$

x2 = -asin(1/8)

$$x_{2} = - \operatorname{asin}{\left(\frac{1}{8} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(1/8) - asin(1/8)

$$- \operatorname{asin}{\left(\frac{1}{8} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{1}{8} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi + asin(1/8))*-asin(1/8)

$$1 \left(\operatorname{asin}{\left(\frac{1}{8} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{8} \right)}\right)$$

=

-(pi + asin(1/8))*asin(1/8)

$$- \left(\operatorname{asin}{\left(\frac{1}{8} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{8} \right)}$$

Численный ответ

x1 = -499.387904089609

x2 = -15.5826354367809

x3 = -78.4144885085768

x4 = -84.6976738157563

x5 = -439.948299333739

x6 = 72.3819588637333

x7 = -65.8481178942176

x8 = -21.8658207439605

x9 = 213.502972612938

x10 = 75.272895854987

x11 = -53.2817472798584

x12 = 22.1164764062966

x13 = -1492.13118262398

x14 = 37.5737840119095

x15 = -94.3731074388619

x16 = 3.26692048475786

x17 = -6.40851313834765

x18 = -0.125327831168065

x19 = -81.8067368245027

x20 = 34.6828470206558

x21 = -9.29945012960131

x22 = -18.9748837527068

x23 = 68.9897105478074

x24 = 81.5560811621666

x25 = 106.688822390885

x26 = 18.7242280903707

x27 = 97.5147000924517

x28 = 31.2905987047299

x29 = -40.7153766654992

x30 = 94.1224517765257

x31 = -28.1490060511401

x32 = 50.1401546262686

x33 = -72.1313032013972

x34 = 47.249217635015

x35 = 6.15785747601152

x36 = 9.55010579193745

x37 = 91.2315147852721

x38 = -3.01626482242173

x39 = 66.0987735565537

x40 = -100.656292746041

x41 = -56.6739955957843

x42 = 59.8155882493741

x43 = 100.405637083705

x44 = -34.4321913583197

x45 = -69.2403662101435

x46 = -46.9985619726788

x47 = -44.1076249814252

x48 = 43.856969319089

x49 = -90.9808591229359

x50 = 12.4410427831911

x51 = -37.8244396742456

x52 = -75.5235515173231

x53 = -25.2580690598864

x54 = 87.8392664693461

x55 = 62.7065252406278

x56 = 84.9483294780925

x57 = -31.541254367066

x58 = -12.6916984455272

x59 = 25.0074133975503

x60 = 56.4233399334482

x61 = 15.833291099117

x62 = 28.3996617134762

x63 = -62.9571809029639

x64 = -50.3908102886048

x65 = 78.6651441709129

x66 = -88.0899221316823

x67 = 40.9660323278354

x68 = 53.5324029421946

x69 = -59.564932587038

x70 = -97.2640444301155

График