cos(x)=(4/5) (уравнение)

Найду корень уравнения: cos(x)=(4/5)

Вы ввели

cos(x) = 4/5

$$\cos{\left(x \right)} = \frac{4}{5}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{4}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{4}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{5} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{4}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{5} \right)}$$
, где n - любое целое число

Сумма и произведение корней

сумма

0 + -acos(4/5) + 2*pi + acos(4/5)

$$\operatorname{acos}{\left(\frac{4}{5} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(4/5) + 2*pi)*acos(4/5)

$$1 \left(- \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{5} \right)}$$

=

(-acos(4/5) + 2*pi)*acos(4/5)

$$\left(- \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{5} \right)}$$

Быстрый ответ

x1 = -acos(4/5) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi$$

x2 = acos(4/5)

$$x_{2} = \operatorname{acos}{\left(\frac{4}{5} \right)}$$

Численный ответ

x1 = 74.7547225773617

x2 = -55.905166655823

x3 = -25.7762423375116

x4 = 88.6080954093075

x5 = 30.7724254271046

x6 = 43.3387960414638

x7 = 63.4753541805892

x8 = 68.4715372701822

x9 = 57.1921688734096

x10 = 3550.64319966526

x11 = 25.7762423375116

x12 = 11.9228695055659

x13 = 44.6257982590504

x14 = 76.0417247949483

x15 = -93.6042784989005

x16 = -101.174466023667

x17 = 87.3210931917209

x18 = -81.0379078845413

x19 = -30.7724254271046

x20 = -38.3426129518708

x21 = -44.6257982590504

x22 = -76.0417247949483

x23 = 0.643501108793284

x24 = -32.0594276446912

x25 = -57.1921688734096

x26 = -74.7547225773617

x27 = -11.9228695055659

x28 = -94.8912807164871

x29 = 38.3426129518708

x30 = 50.90898356623

x31 = -62.1883519630026

x32 = -63.4753541805892

x33 = -99.8874638060801

x34 = 93.6042784989005

x35 = -49.6219813486434

x36 = -82.3249101021279

x37 = 32.0594276446912

x38 = 24.4892401199251

x39 = -87.3210931917209

x40 = -3210.06419085998

x41 = -88.6080954093075

x42 = -37.0556107342842

x43 = -50.90898356623

x44 = -19.493057030332

x45 = 94.8912807164871

x46 = -69.7585394877687

x47 = -68.4715372701822

x48 = 6.92668641597287

x49 = -6.92668641597287

x50 = 69.7585394877687

x51 = 82.3249101021279

x52 = -24.4892401199251

x53 = 55.905166655823

x54 = 99.8874638060801

x55 = -13.2098717231525

x56 = 19.493057030332

x57 = 49.6219813486434

x58 = 13.2098717231525

x59 = -5.6396841983863

x60 = -12486222.9460819

x61 = 18.2060548127455

x62 = 81.0379078845413

x63 = 37.0556107342842

x64 = -43.3387960414638

x65 = -0.643501108793284

x66 = -18.2060548127455

x67 = 5.6396841983863

x68 = 62.1883519630026

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