4*sin(x)=-1 (уравнение)

Найду корень уравнения: 4*sin(x)=-1

Вы ввели

4*sin(x) = -1

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

Подробное решение

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

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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -15.4552830128069

x2 = -34.3048389343456

x3 = -59.437580163064

x4 = -270.429648463864

x5 = 53.6597553661686

x6 = 31.1632462807559

x7 = 87.7119140453721

x8 = -50.5181627125788

x9 = 75.145543431013

x10 = -97.1366920061415

x11 = -53.1543948558844

x12 = -37.9517920982196

x13 = -19.1022361766808

x14 = 100.278284659731

x15 = -81.9340892484767

x16 = 15.960643523091

x17 = -90.8535066989619

x18 = 47.376570058989

x19 = 50.0128022022946

x20 = -28.0216536271661

x21 = 41.0933847518094

x22 = -65.7207654702436

x23 = 66.2261259805277

x24 = -72.0039507774232

x25 = -2.88891239844771

x26 = 93.9950993525517

x27 = 22.2438288302706

x28 = 34.8101994446298

x29 = -78.2871360846027

x30 = 6.03050505203751

x31 = -9.1720977056273

x32 = -75.6509039412971

x33 = -46.8712095487048

x34 = -40.5880242415252

x35 = -44.2349774053992

x36 = 9.67745821591146

x37 = -100.783645170015

x38 = -56.8013480197584

x39 = 72.5093112877073

x40 = 62.5791728166538

x41 = 24.8800609735763

x42 = -31.66860679104

x43 = 85.0756819020665

x44 = 12.3136903592171

x45 = -88.2172745556563

x46 = -25.3854214838604

x47 = 91.3588672092461

x48 = 190160.350641535

x49 = -84.5703213917823

x50 = 3.39427290873187

x51 = -6.53586556232167

x52 = 97.6420525164257

x53 = 37.4464315879354

x54 = -21.7384683199865

x55 = -0.252680255142079

x56 = -12.8190508695013

x57 = 81.4287287381925

x58 = -69.3677186341175

x59 = 59.9429406733481

x60 = 28.5270141374502

x61 = 78.7924965948869

x62 = 43.729616895115

x63 = 18.5968756663967

x64 = -63.0845333269379

x65 = -94.5004598628359

x66 = 68.8623581238334

x67 = 56.2959875094742

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