(4sinx-1)=0 (уравнение)

Найду корень уравнения: (4sinx-1)=0

Вы ввели

4*sin(x) - 1 = 0

$$4 \sin{\left(x \right)} - 1 = 0$$

Подробное решение

Дано уравнение
$$4 \sin{\left(x \right)} - 1 = 0$$
- это простейшее тригонометрическое ур-ние

Перенесём -1 в правую часть ур-ния

с изменением знака при -1

Получим:
$$4 \sin{\left(x \right)} - 1 + 1 = 1$$

Разделим обе части ур-ния на 4

Ур-ние превратится в
$$\sin{\left(x \right)} = \frac{1}{4}$$
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 = -97.6420525164257

x2 = 53.1543948558844

x3 = -41.0933847518094

x4 = 12.8190508695013

x5 = 44.2349774053992

x6 = 94.5004598628359

x7 = 2.88891239844771

x8 = 88.2172745556563

x9 = -43.729616895115

x10 = 19.1022361766808

x11 = -93.9950993525517

x12 = -56.2959875094742

x13 = 9.1720977056273

x14 = 50.5181627125788

x15 = -100.278284659731

x16 = 25.3854214838604

x17 = -85.0756819020665

x18 = -91.3588672092461

x19 = 28.0216536271661

x20 = -28.5270141374502

x21 = 15.4552830128069

x22 = -31.1632462807559

x23 = 56.8013480197584

x24 = -62.5791728166538

x25 = 65.7207654702436

x26 = 75.6509039412971

x27 = 84.5703213917823

x28 = 90.8535066989619

x29 = -116.491608437964

x30 = -12.3136903592171

x31 = -87.7119140453721

x32 = 31.66860679104

x33 = -59.9429406733481

x34 = -24.8800609735763

x35 = 0.252680255142079

x36 = -9.67745821591146

x37 = -6.03050505203751

x38 = -3.39427290873187

x39 = -22.2438288302706

x40 = 78.2871360846027

x41 = -72.5093112877073

x42 = 21.7384683199865

x43 = 59.437580163064

x44 = 81.9340892484767

x45 = 63.0845333269379

x46 = -47.376570058989

x47 = 6.53586556232167

x48 = -50.0128022022946

x49 = -15.960643523091

x50 = 46.8712095487048

x51 = 163.615498241811

x52 = -68.8623581238334

x53 = 144.765942320273

x54 = -81.4287287381925

x55 = -37.4464315879354

x56 = -66.2261259805277

x57 = -18.5968756663967

x58 = -34.8101994446298

x59 = 34.3048389343456

x60 = -75.145543431013

x61 = 37.9517920982196

x62 = 100.783645170015

x63 = 97.1366920061415

x64 = 40.5880242415252

x65 = -78.7924965948869

x66 = 72.0039507774232

x67 = -53.6597553661686

x68 = 69.3677186341175

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