sin(x)=2/10 (уравнение)

Найду корень уравнения: sin(x)=2/10

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 = 78.3384584189545

x2 = -87.7632363797239

x3 = 31.6172844566883

x4 = 2.94023473279946

x5 = 12.7677285351495

x6 = 90.9048290333137

x7 = -53.6084330318168

x8 = -24.931383307928

x9 = -41.0420624174576

x10 = 19.0509138423291

x11 = 81.882766914125

x12 = -2814.66565969566

x13 = 53.2057171902362

x14 = 9.22342003997905

x15 = -28.4756918030985

x16 = 21.7897906543382

x17 = 46.9225318830566

x18 = 97.1880143404933

x19 = 88.1659522213045

x20 = -22.1925064959189

x21 = -188.294201294597

x22 = 72.0552731117749

x23 = -100.329606994083

x24 = 44.1836550710474

x25 = -56.3473098438259

x26 = 100.732322835664

x27 = -59.8916183389964

x28 = 56.7500256854066

x29 = -66.174803646176

x30 = 65.7720878045953

x31 = -62.6304951510055

x32 = -37.4977539222872

x33 = 63.0332109925862

x34 = -1746.52415747513

x35 = 50.466840378227

x36 = 15.5066053471586

x37 = 6.48454322796992

x38 = 40.639346575877

x39 = -97.5907301820739

x40 = -75.1968657653647

x41 = -18.6481980007484

x42 = -12.3650126935688

x43 = -43.7809392294668

x44 = 84.6216437261341

x45 = -348.918142469257

x46 = 0.201357920790331

x47 = 25.3340991495087

x48 = -68.9136804581851

x49 = -78.7411742605352

x50 = 75.5995816069454

x51 = 69.3163962997658

x52 = -85.0243595677148

x53 = -15.9093211887393

x54 = -81.4800510725443

x55 = -50.0641245366464

x56 = 37.9004697638678

x57 = -47.3252477246372

x58 = -6.08182738638926

x59 = -72.4579889533556

x60 = -94.0464216869035

x61 = 28.0729759615178

x62 = 59.4889024974157

x63 = -9.62613588155971

x64 = -91.3075448748943

x65 = -31.2145686151076

x66 = -34.7588771102781

x67 = 34.3561612686974

x68 = 94.4491375284841

x69 = -3.34295057438012

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