cos(x)=-0,9 (уравнение)

Найду корень уравнения: cos(x)=-0,9

Вы ввели

cos(x) = -9/10

$$\cos{\left(x \right)} = - \frac{9}{10}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{9}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{9}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{9}{10} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{9}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{9}{10} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-9/10) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{9}{10} \right)} + 2 \pi$$

x2 = acos(-9/10)

$$x_{2} = \operatorname{acos}{\left(- \frac{9}{10} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-9/10) + 2*pi + acos(-9/10)

$$\operatorname{acos}{\left(- \frac{9}{10} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{9}{10} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-9/10) + 2*pi)*acos(-9/10)

$$1 \left(- \operatorname{acos}{\left(- \frac{9}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{9}{10} \right)}$$

=

(-acos(-9/10) + 2*pi)*acos(-9/10)

$$\left(- \operatorname{acos}{\left(- \frac{9}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{9}{10} \right)}$$

Численный ответ

x1 = -72.7076578443615

x2 = -97.8403990730799

x3 = -66.4244725371819

x4 = 59.2392336064098

x5 = 84.3719748351282

x6 = -84.3719748351282

x7 = -34.1064923776915

x8 = 41.2917313084636

x9 = -1863.41547039054

x10 = 8.97375114897312

x11 = 16.1589900797452

x12 = -78.0887895279486

x13 = -71.805604220769

x14 = 65.5224189135894

x15 = -35.008546001284

x16 = 53.8581019228227

x17 = 46.6728629920506

x18 = 21.5401217633323

x19 = 85.2740284587207

x20 = 316015.495590439

x21 = -2.69056584179353

x22 = 34.1064923776915

x23 = 9.87580477256564

x24 = -27.8233070705119

x25 = 90.6551601423077

x26 = -638.194335490524

x27 = -28.7253606941044

x28 = -8.97375114897312

x29 = 512.530629346933

x30 = -21.5401217633323

x31 = -65.5224189135894

x32 = -52.9560482992302

x33 = 15.2569364561527

x34 = -9.87580477256564

x35 = -624.725911252573

x36 = -91.5572137659003

x37 = -40.3896776848711

x38 = -41.2917313084636

x39 = 40.3896776848711

x40 = -15.2569364561527

x41 = -60.1412872300023

x42 = 78.0887895279486

x43 = 27.8233070705119

x44 = 78.9908431515411

x45 = 71.805604220769

x46 = 72.7076578443615

x47 = 97.8403990730799

x48 = 2.69056584179353

x49 = -22.4421753869248

x50 = 52.9560482992302

x51 = 96.9383454494873

x52 = -78.9908431515411

x53 = -47.5749166156432

x54 = 35.008546001284

x55 = 8171.73351879885

x56 = -90.6551601423077

x57 = -46.6728629920506

x58 = -85.2740284587207

x59 = -53.8581019228227

x60 = 3.59261946538606

x61 = 60.1412872300023

x62 = 28.7253606941044

x63 = 47.5749166156432

x64 = 91.5572137659003

x65 = -10710.1403828994

x66 = 22.4421753869248

x67 = -59.2392336064098

x68 = -96.9383454494873

x69 = -16.1589900797452

x70 = -3.59261946538606

x71 = 66.4244725371819

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