sinx=0,36 (уравнение)

Найду корень уравнения: sinx=0,36

Вы ввели

sin(x) = 9/25

$$\sin{\left(x \right)} = \frac{9}{25}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{9}{25}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{9}{25} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{9}{25} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{9}{25} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{9}{25} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(9/25)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{9}{25} \right)}$$

x2 = asin(9/25)

$$x_{2} = \operatorname{asin}{\left(\frac{9}{25} \right)}$$

Сумма и произведение корней

сумма

pi - asin(9/25) + asin(9/25)

$$\operatorname{asin}{\left(\frac{9}{25} \right)} + \left(\pi - \operatorname{asin}{\left(\frac{9}{25} \right)}\right)$$

=

pi

$$\pi$$

произведение

(pi - asin(9/25))*asin(9/25)

$$\left(\pi - \operatorname{asin}{\left(\frac{9}{25} \right)}\right) \operatorname{asin}{\left(\frac{9}{25} \right)}$$

=

(pi - asin(9/25))*asin(9/25)

$$\left(\pi - \operatorname{asin}{\left(\frac{9}{25} \right)}\right) \operatorname{asin}{\left(\frac{9}{25} \right)}$$

Численный ответ

x1 = 56.9169356580529

x2 = 50.6337503508733

x3 = -53.7753430044631

x4 = 71.8883631391286

x5 = 69.4833062724121

x6 = -5.91491741374295

x7 = -91.4744548475406

x8 = 46.7556219104103

x9 = 97.0211043678469

x10 = 21.6228806816919

x11 = -49.8972145640001

x12 = -31.0476586424613

x13 = 63.2001209652325

x14 = -81.313141099898

x15 = -18.4812880281021

x16 = 15.3396953745123

x17 = 53.0388072175898

x18 = 2.77332476015315

x19 = -78549.609385599

x20 = -47.4921576972835

x21 = -72.6248989260019

x22 = -66.3417136188223

x23 = -56.1803998711796

x24 = -75.0299557927184

x25 = 19.2178238149754

x26 = 59.3219925247694

x27 = -41.208972390104

x28 = 75.7664915795917

x29 = 40.4724366032307

x30 = -37.3308439496409

x31 = 12.9346385077958

x32 = -9.79304585420602

x33 = -85.1912695403611

x34 = 88.3328621939508

x35 = -100.162697021437

x36 = -3.50986054702643

x37 = 25.501009122155

x38 = -62.4635851783592

x39 = 94.6160475011304

x40 = -311.385940598826

x41 = -60.0585283116427

x42 = 38.0673797365142

x43 = 34.1892512960511

x44 = -97.7576401547202

x45 = -24.7644733352817

x46 = 84.4547337534878

x47 = -34.9257870829244

x48 = 27.9060659888715

x49 = -87.5963264070776

x50 = 90.7379190606674

x51 = 166.136142746822

x52 = 44.3505650436937

x53 = -16.0762311613856

x54 = -12.1981027209225

x55 = 6.65145320061623

x56 = -28.6426017757448

x57 = 31.7841944293346

x58 = 9.05651006733274

x59 = -43.6140292568205

x60 = 0.36826789343664

x61 = -93.8795117142572

x62 = -22.3594164685652

x63 = -78.9080842331815

x64 = 100.89923280831

x65 = 78.1715484463082

x66 = 65.605177831949

x67 = 82.0496768867713

x68 = -68.7467704855388

График