sinx=-1/4 (уравнение)

Найду корень уравнения: sinx=-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)

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

x2 = -asin(1/4)

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

Сумма и произведение корней

сумма

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

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

=

pi

$$\pi$$

произведение

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

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

=

-(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 = -84.5703213917823

x2 = 9.67745821591146

x3 = 12.3136903592171

x4 = -34.3048389343456

x5 = -90.8535066989619

x6 = 85.0756819020665

x7 = 87.7119140453721

x8 = 24.8800609735763

x9 = 100.278284659731

x10 = -65.7207654702436

x11 = -270.429648463864

x12 = 15.960643523091

x13 = 81.4287287381925

x14 = -59.437580163064

x15 = -9.1720977056273

x16 = 91.3588672092461

x17 = 78.7924965948869

x18 = -97.1366920061415

x19 = 41.0933847518094

x20 = -100.783645170015

x21 = -88.2172745556563

x22 = -50.5181627125788

x23 = -72.0039507774232

x24 = -75.6509039412971

x25 = -46.8712095487048

x26 = -69.3677186341175

x27 = -37.9517920982196

x28 = -28.0216536271661

x29 = -40.5880242415252

x30 = 50.0128022022946

x31 = 53.6597553661686

x32 = 37.4464315879354

x33 = 22.2438288302706

x34 = 56.2959875094742

x35 = -0.252680255142079

x36 = -81.9340892484767

x37 = -21.7384683199865

x38 = -6.53586556232167

x39 = -31.66860679104

x40 = 34.8101994446298

x41 = 93.9950993525517

x42 = -53.1543948558844

x43 = -25.3854214838604

x44 = 75.145543431013

x45 = -63.0845333269379

x46 = 68.8623581238334

x47 = -12.8190508695013

x48 = 59.9429406733481

x49 = 43.729616895115

x50 = -19.1022361766808

x51 = -78.2871360846027

x52 = -44.2349774053992

x53 = 31.1632462807559

x54 = -2.88891239844771

x55 = 66.2261259805277

x56 = 3.39427290873187

x57 = 190160.350641535

x58 = 72.5093112877073

x59 = 47.376570058989

x60 = 6.03050505203751

x61 = 97.6420525164257

x62 = -56.8013480197584

x63 = 18.5968756663967

x64 = -15.4552830128069

x65 = 28.5270141374502

x66 = -94.5004598628359

x67 = 62.5791728166538

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