sin(x)=1/4 (уравнение)

Найду корень уравнения: sin(x)=1/4

Вы ввели

sin(x) = 1/4

$$\sin{\left(x \right)} = \frac{1}{4}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{1}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{4} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{4} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(1/4)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{4} \right)}$$

x2 = asin(1/4)

$$x_{2} = \operatorname{asin}{\left(\frac{1}{4} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(1/4) + asin(1/4)

$$\operatorname{asin}{\left(\frac{1}{4} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{4} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(1/4))*asin(1/4)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{4} \right)}\right) \operatorname{asin}{\left(\frac{1}{4} \right)}$$

=

(pi - asin(1/4))*asin(1/4)

$$\left(\pi - \operatorname{asin}{\left(\frac{1}{4} \right)}\right) \operatorname{asin}{\left(\frac{1}{4} \right)}$$

Численный ответ

x1 = 81.9340892484767

x2 = -91.3588672092461

x3 = -31.1632462807559

x4 = -66.2261259805277

x5 = -81.4287287381925

x6 = -56.2959875094742

x7 = 90.8535066989619

x8 = 63.0845333269379

x9 = 100.783645170015

x10 = 9.1720977056273

x11 = -6.03050505203751

x12 = -50.0128022022946

x13 = -116.491608437964

x14 = -72.5093112877073

x15 = 53.1543948558844

x16 = -59.9429406733481

x17 = 56.8013480197584

x18 = -85.0756819020665

x19 = 50.5181627125788

x20 = -43.729616895115

x21 = -3.39427290873187

x22 = -87.7119140453721

x23 = 44.2349774053992

x24 = 88.2172745556563

x25 = 19.1022361766808

x26 = 40.5880242415252

x27 = 6.53586556232167

x28 = 2.88891239844771

x29 = 12.8190508695013

x30 = -100.278284659731

x31 = -41.0933847518094

x32 = -12.3136903592171

x33 = 84.5703213917823

x34 = 163.615498241811

x35 = -47.376570058989

x36 = -9.67745821591146

x37 = 21.7384683199865

x38 = -78.7924965948869

x39 = -22.2438288302706

x40 = 59.437580163064

x41 = -18.5968756663967

x42 = -62.5791728166538

x43 = -97.6420525164257

x44 = -93.9950993525517

x45 = -34.8101994446298

x46 = 28.0216536271661

x47 = 46.8712095487048

x48 = 0.252680255142079

x49 = 34.3048389343456

x50 = 65.7207654702436

x51 = -68.8623581238334

x52 = -37.4464315879354

x53 = 72.0039507774232

x54 = 144.765942320273

x55 = 75.6509039412971

x56 = 15.4552830128069

x57 = 78.2871360846027

x58 = -28.5270141374502

x59 = 25.3854214838604

x60 = -15.960643523091

x61 = 69.3677186341175

x62 = 97.1366920061415

x63 = 37.9517920982196

x64 = 31.66860679104

x65 = -53.6597553661686

x66 = -75.145543431013

x67 = -24.8800609735763

x68 = 94.5004598628359

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