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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = -69.3163962997658

x2 = 85.0243595677148

x3 = 91.3075448748943

x4 = -100.732322835664

x5 = 50.0641245366464

x6 = -28.0729759615178

x7 = 43.7809392294668

x8 = 9845.55001842962

x9 = -40.639346575877

x10 = 47.3252477246372

x11 = -37.9004697638678

x12 = -78.3384584189545

x13 = 225.993313137675

x14 = 15.9093211887393

x15 = 28.4756918030985

x16 = 34.7588771102781

x17 = -12.7677285351495

x18 = -50.466840378227

x19 = 81.4800510725443

x20 = -6.48454322796992

x21 = 66.174803646176

x22 = 3.34295057438012

x23 = -31.6172844566883

x24 = -75.5995816069454

x25 = 56.3473098438259

x26 = -9.22342003997905

x27 = -90.9048290333137

x28 = 3845.10805007312

x29 = 6.08182738638926

x30 = 12.3650126935688

x31 = 22.1925064959189

x32 = -21.7897906543382

x33 = 59.8916183389964

x34 = -81.882766914125

x35 = 68.9136804581851

x36 = -15.5066053471586

x37 = 24.931383307928

x38 = -46.9225318830566

x39 = 100.329606994083

x40 = 129.006656717972

x41 = -0.201357920790331

x42 = 18.6481980007484

x43 = -2.94023473279946

x44 = -88.1659522213045

x45 = -19.0509138423291

x46 = 172.988953868229

x47 = 87.7632363797239

x48 = 97.5907301820739

x49 = -107.015508142843

x50 = -59.4889024974157

x51 = -97.1880143404933

x52 = -56.7500256854066

x53 = -279.400388248701

x54 = -94.4491375284841

x55 = 9.62613588155971

x56 = 62.6304951510055

x57 = -84.6216437261341

x58 = 37.4977539222872

x59 = 31.2145686151076

x60 = 41.0420624174576

x61 = 53.6084330318168

x62 = -63.0332109925862

x63 = 72.4579889533556

x64 = -53.2057171902362

x65 = -25.3340991495087

x66 = -34.3561612686974

x67 = 78.7411742605352

x68 = 75.1968657653647

x69 = -65.7720878045953

x70 = -72.0552731117749

x71 = 4024.58154716932

x72 = -44.1836550710474

x73 = 94.0464216869035

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