sin(x)=1/7 (уравнение)

Найду корень уравнения: sin(x)=1/7

Вы ввели

sin(x) = 1/7

$$\sin{\left(x \right)} = \frac{1}{7}$$

Подробное решение

Дано уравнение
$$\sin{\left(x \right)} = \frac{1}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{7} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{7} \right)} + \pi$$
, где n - любое целое число

Сумма и произведение корней

сумма

0 + pi - asin(1/7) + asin(1/7)

$$\operatorname{asin}{\left(\frac{1}{7} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{1}{7} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(1/7))*asin(1/7)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{1}{7} \right)}\right) \operatorname{asin}{\left(\frac{1}{7} \right)}$$

=

(pi - asin(1/7))*asin(1/7)

$$\left(\pi - \operatorname{asin}{\left(\frac{1}{7} \right)}\right) \operatorname{asin}{\left(\frac{1}{7} \right)}$$

Быстрый ответ

x1 = pi - asin(1/7)

$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{7} \right)}$$

x2 = asin(1/7)

$$x_{2} = \operatorname{asin}{\left(\frac{1}{7} \right)}$$

Численный ответ

x1 = 34.4141716205824

x2 = -18.7062083526334

x3 = -62.6885055028905

x4 = 40.6973569277619

x5 = 18.9929034904441

x6 = -91.2495345230094

x7 = 72.1132834636599

x8 = -47.2672373727523

x9 = -43.8389495813517

x10 = -6.13983773827422

x11 = -94.1044320387884

x12 = -72.3999786014706

x13 = 2.99824508468443

x14 = 31.5592741048033

x15 = -81.5380614244293

x16 = 97.2460246923782

x17 = 21.8478010062232

x18 = 75.5415712550604

x19 = -37.5557642741722

x20 = -87.8212467316089

x21 = 69.2583859478808

x22 = -110.099090444548

x23 = 15.5646156990436

x24 = 84.6796540780191

x25 = 12.7097181832645

x26 = 59.5469128493007

x27 = 88.1079418694196

x28 = -31.2725789669926

x29 = 46.9805422349415

x30 = 65.8300981564803

x31 = 78.3964687708395

x32 = 81.82475656224

x33 = -9.56812552967475

x34 = -75.2548761172497

x35 = -12.4230230454538

x36 = 907.776929318545

x37 = -53.5504226799318

x38 = -78.6831639086502

x39 = -15.8513108368543

x40 = 37.8424594119829

x41 = -56.4053201957109

x42 = 6.42653287608495

x43 = 44.1256447191625

x44 = 25.2760887976237

x45 = 94.3911271765992

x46 = 100.674312483779

x47 = -3.28494022249516

x48 = -34.7008667583931

x49 = 90.9628393851986

x50 = 28.1309863134028

x51 = 50.4088300263421

x52 = -122.665461058907

x53 = -22.1344961440339

x54 = -50.1221348885313

x55 = -100.387617345968

x56 = 62.9752006407012

x57 = -97.532719830189

x58 = -84.9663492158298

x59 = 0.143347568905365

x60 = 9.28143039186401

x61 = -59.8336079871114

x62 = -66.116793294291

x63 = -28.4176814512135

x64 = 56.6920153335216

x65 = -40.9840520655727

x66 = -68.9716908100701

x67 = -24.989393659813

x68 = -128.948646366087

x69 = 53.2637275421211

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