sin(x)=0.2 (уравнение)

Найду корень уравнения: sin(x)=0.2

Вы ввели

sin(x) = 1/5

$$\sin{\left(x \right)} = \frac{1}{5}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{1}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

x1 = pi - asin(1/5)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{5} \right)}$$

x2 = asin(1/5)

$$x_{2} = \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(1/5) + asin(1/5)

$$\operatorname{asin}{\left(\frac{1}{5} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(1/5))*asin(1/5)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$

=

(pi - asin(1/5))*asin(1/5)

$$\left(\pi - \operatorname{asin}{\left(\frac{1}{5} \right)}\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Численный ответ

x1 = 28.0729759615178

x2 = -85.0243595677148

x3 = -34.7588771102781

x4 = -188.294201294597

x5 = -41.0420624174576

x6 = -68.9136804581851

x7 = -37.4977539222872

x8 = 81.882766914125

x9 = -22.1925064959189

x10 = 31.6172844566883

x11 = 0.201357920790331

x12 = -31.2145686151076

x13 = 100.732322835664

x14 = 46.9225318830566

x15 = -50.0641245366464

x16 = 9.22342003997905

x17 = -9.62613588155971

x18 = 19.0509138423291

x19 = -56.3473098438259

x20 = 34.3561612686974

x21 = 50.466840378227

x22 = 21.7897906543382

x23 = 37.9004697638678

x24 = 84.6216437261341

x25 = 59.4889024974157

x26 = 72.0552731117749

x27 = 53.2057171902362

x28 = -6.08182738638926

x29 = -72.4579889533556

x30 = 40.639346575877

x31 = -3.34295057438012

x32 = -91.3075448748943

x33 = -2814.66565969566

x34 = 2.94023473279946

x35 = -24.931383307928

x36 = -53.6084330318168

x37 = 78.3384584189545

x38 = 88.1659522213045

x39 = 97.1880143404933

x40 = -100.329606994083

x41 = 56.7500256854066

x42 = 65.7720878045953

x43 = -18.6481980007484

x44 = 69.3163962997658

x45 = 12.7677285351495

x46 = -94.0464216869035

x47 = 44.1836550710474

x48 = -348.918142469257

x49 = -59.8916183389964

x50 = 6.48454322796992

x51 = 90.9048290333137

x52 = -47.3252477246372

x53 = 63.0332109925862

x54 = -62.6304951510055

x55 = -75.1968657653647

x56 = -1746.52415747513

x57 = -97.5907301820739

x58 = -66.174803646176

x59 = -78.7411742605352

x60 = -28.4756918030985

x61 = 15.5066053471586

x62 = -43.7809392294668

x63 = -15.9093211887393

x64 = 75.5995816069454

x65 = -87.7632363797239

x66 = -12.3650126935688

x67 = -81.4800510725443

x68 = 94.4491375284841

x69 = 25.3340991495087

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