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

Быстрый ответ

x1 = pi + asin(1/7)

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

x2 = -asin(1/7)

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

Сумма и произведение корней

сумма

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

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

x1 = 72.3999786014706

x2 = 40.9840520655727

x3 = -50.4088300263421

x4 = -37.8424594119829

x5 = 6.13983773827422

x6 = -2.99824508468443

x7 = -72.1132834636599

x8 = 68.9716908100701

x9 = 66.116793294291

x10 = 62.6885055028905

x11 = 34.7008667583931

x12 = -56.6920153335216

x13 = 37.5557642741722

x14 = 298.594649659936

x15 = -44.1256447191625

x16 = 15.8513108368543

x17 = -12.7097181832645

x18 = 81.5380614244293

x19 = -18.9929034904441

x20 = -62.9752006407012

x21 = 24.989393659813

x22 = 47.2672373727523

x23 = 100.387617345968

x24 = -31.5592741048033

x25 = -88.1079418694196

x26 = 9.56812552967475

x27 = 50.1221348885313

x28 = -53.2637275421211

x29 = -34.4141716205824

x30 = 31.2725789669926

x31 = -40.6973569277619

x32 = -103.529209999558

x33 = 84.9663492158298

x34 = 78.6831639086502

x35 = 94.1044320387884

x36 = 97.532719830189

x37 = -46.9805422349415

x38 = 28.4176814512135

x39 = -28.1309863134028

x40 = -75.5415712550604

x41 = 263.750435332637

x42 = -6.42653287608495

x43 = 12.4230230454538

x44 = -69.2583859478808

x45 = -97.2460246923782

x46 = 59.8336079871114

x47 = -90.9628393851986

x48 = -65.8300981564803

x49 = -59.5469128493007

x50 = -84.6796540780191

x51 = 43.8389495813517

x52 = -15.5646156990436

x53 = -9.28143039186401

x54 = 3.28494022249516

x55 = 56.4053201957109

x56 = -94.3911271765992

x57 = 87.8212467316089

x58 = 75.2548761172497

x59 = -21.8478010062232

x60 = 18.7062083526334

x61 = 53.5504226799318

x62 = -81.82475656224

x63 = -78.3964687708395

x64 = -0.143347568905365

x65 = 91.2495345230094

x66 = -100.674312483779

x67 = -25.2760887976237

x68 = 22.1344961440339

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