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 = 25.5837680405146

x2 = -6.73421211897585

x3 = -88.4156211123105

x4 = 44.4333239620534

x5 = -24.6817144169221

x6 = -50.716509269233

x7 = 63.2828798835921

x8 = 19.300582733335

x9 = -100.98199172667

x10 = -38.1501386548738

x11 = 56.9996945764125

x12 = -49.8144556456404

x13 = -94.6988064194901

x14 = 12.1153438025629

x15 = 82.1324358051309

x16 = 74.9471968743588

x17 = 49.8144556456404

x18 = 584.787260379498

x19 = -19.300582733335

x20 = -100.079938103077

x21 = 50.716509269233

x22 = -93.7967527958975

x23 = -37.2480850312813

x24 = 87.513567488718

x25 = 5.83215849538332

x26 = -12.1153438025629

x27 = 31.8669533476942

x28 = -87.513567488718

x29 = -63.2828798835921

x30 = 88.4156211123105

x31 = 81.2303821815384

x32 = 69.5660651907717

x33 = 13138.5915041243

x34 = -56.9996945764125

x35 = -31.8669533476942

x36 = 37.2480850312813

x37 = 62.3808262599996

x38 = 24.6817144169221

x39 = -0.451026811796262

x40 = -75.8492504979513

x41 = 188.946586027184

x42 = -68.6640115671792

x43 = 100.079938103077

x44 = 1621.51283606413

x45 = -25.5837680405146

x46 = -13.0173974261554

x47 = 94.6988064194901

x48 = 144.062235253334

x49 = 68.6640115671792

x50 = 30.9648997241017

x51 = -30.9648997241017

x52 = -44.4333239620534

x53 = -62.3808262599996

x54 = -56.09764095282

x55 = -43.5312703384608

x56 = -69.5660651907717

x57 = -1476.09752037541

x58 = 56.09764095282

x59 = -74.9471968743588

x60 = 38.1501386548738

x61 = 43.5312703384608

x62 = 93.7967527958975

x63 = 0.451026811796262

x64 = 6.73421211897585

x65 = -5.83215849538332

x66 = 13.0173974261554

x67 = 18.3985291097425

x68 = 75.8492504979513

x69 = -18.3985291097425

x70 = -82.1324358051309

x71 = -81.2303821815384

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