cos(x)=0.7 (уравнение)

Найду корень уравнения: cos(x)=0.7

Вы ввели

cos(x) = 7/10

$$\cos{\left(x \right)} = \frac{7}{10}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{7}{10}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{7}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{7}{10} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{7}{10} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{7}{10} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(7/10) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{7}{10} \right)} + 2 \pi$$

x2 = acos(7/10)

$$x_{2} = \operatorname{acos}{\left(\frac{7}{10} \right)}$$

Сумма и произведение корней

сумма

-acos(7/10) + 2*pi + acos(7/10)

$$\operatorname{acos}{\left(\frac{7}{10} \right)} + \left(- \operatorname{acos}{\left(\frac{7}{10} \right)} + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

(-acos(7/10) + 2*pi)*acos(7/10)

$$\left(- \operatorname{acos}{\left(\frac{7}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{7}{10} \right)}$$

=

(-acos(7/10) + 2*pi)*acos(7/10)

$$\left(- \operatorname{acos}{\left(\frac{7}{10} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{7}{10} \right)}$$

Численный ответ

x1 = 62.0364542416117

x2 = -1967.43239997739

x3 = 19.6449547517229

x4 = -2424.51412974114

x5 = 63.62725190198

x6 = -76.1936225163392

x7 = -99.7355660846892

x8 = 88.7599931306983

x9 = 82.4768078235188

x10 = -63.62725190198

x11 = 51.0608812876208

x12 = -38.4945106732617

x13 = 13.3617694445433

x14 = 57.3440665948004

x15 = 7088.22842532876

x16 = -82.4768078235188

x17 = -43.186898320073

x18 = 99.7355660846892

x19 = -68.3196395487913

x20 = -69.9104372091596

x21 = -5.48778647699544

x22 = 11.770971784175

x23 = -74.6028248559709

x24 = -11.770971784175

x25 = 0.795398830184144

x26 = 74.6028248559709

x27 = 49.4700836272525

x28 = -80.8860101631505

x29 = 76.1936225163392

x30 = 87.1691954703301

x31 = -44.7776959804413

x32 = -87.1691954703301

x33 = 80.8860101631505

x34 = 55.7532689344321

x35 = -0.795398830184144

x36 = 93.4523807775097

x37 = 38.4945106732617

x38 = -36.9037130128934

x39 = -95.0431784378779

x40 = -18.0541570913546

x41 = -32.2113253660821

x42 = -55.7532689344321

x43 = 68.3196395487913

x44 = -62.0364542416117

x45 = 69.9104372091596

x46 = 30.6205277057138

x47 = -57.3440665948004

x48 = 44.7776959804413

x49 = -7.07858413736373

x50 = -13.3617694445433

x51 = -30.6205277057138

x52 = 25.9281400589025

x53 = 32.2113253660821

x54 = 7.07858413736373

x55 = -19.6449547517229

x56 = 24.3373423985342

x57 = -24.3373423985342

x58 = -93.4523807775097

x59 = 5.48778647699544

x60 = -51.0608812876208

x61 = 43.186898320073

x62 = 36.9037130128934

x63 = -25.9281400589025

x64 = -88.7599931306983

x65 = -49.4700836272525

x66 = 18.0541570913546

x67 = -101.326363745058

x68 = 95.0431784378779

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