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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -68.9897105478074

x2 = -97.5147000924517

x3 = 37.8244396742456

x4 = -78.6651441709129

x5 = 18.9748837527068

x6 = -91.2315147852721

x7 = 69.2403662101435

x8 = -56.4233399334482

x9 = -9.55010579193745

x10 = 50.3908102886048

x11 = -100.405637083705

x12 = -50.1401546262686

x13 = -53.5324029421946

x14 = -12.4410427831911

x15 = 56.6739955957843

x16 = -31.2905987047299

x17 = -62.7065252406278

x18 = 84.6976738157563

x19 = 12.6916984455272

x20 = 62.9571809029639

x21 = 53.2817472798584

x22 = 21.8658207439605

x23 = -34.6828470206558

x24 = -84.9483294780925

x25 = -94.1224517765257

x26 = 3.01626482242173

x27 = 75.5235515173231

x28 = 34.4321913583197

x29 = 9.29945012960131

x30 = -18.7242280903707

x31 = 40.7153766654992

x32 = -59.8155882493741

x33 = 44.1076249814252

x34 = 72.1313032013972

x35 = -66.0987735565537

x36 = 59.564932587038

x37 = -37.5737840119095

x38 = 97.2640444301155

x39 = -3.26692048475786

x40 = -47.249217635015

x41 = -6.15785747601152

x42 = 15.5826354367809

x43 = 0.125327831168065

x44 = 90.9808591229359

x45 = 81.8067368245027

x46 = -15.833291099117

x47 = -22.1164764062966

x48 = -25.0074133975503

x49 = -147.780182549888

x50 = 25.2580690598864

x51 = 46.9985619726788

x52 = -43.856969319089

x53 = 31.541254367066

x54 = -72.3819588637333

x55 = 65.8481178942176

x56 = 103.547229737295

x57 = -87.8392664693461

x58 = 88.0899221316823

x59 = 6.40851313834765

x60 = 4181.33449409685

x61 = -28.3996617134762

x62 = 94.3731074388619

x63 = 144.638589896299

x64 = 28.1490060511401

x65 = -40.9660323278354

x66 = -75.272895854987

x67 = 78.4144885085768

x68 = 100.656292746041

x69 = -81.5560811621666

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