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

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

$$\operatorname{acos}{\left(\frac{7}{10} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{7}{10} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

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

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

=

(-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 = 99.7355660846892

x2 = 36.9037130128934

x3 = -69.9104372091596

x4 = 11.770971784175

x5 = -80.8860101631505

x6 = -76.1936225163392

x7 = -0.795398830184144

x8 = -24.3373423985342

x9 = -55.7532689344321

x10 = -57.3440665948004

x11 = -7.07858413736373

x12 = -2424.51412974114

x13 = 32.2113253660821

x14 = -44.7776959804413

x15 = -74.6028248559709

x16 = 49.4700836272525

x17 = 24.3373423985342

x18 = -68.3196395487913

x19 = 0.795398830184144

x20 = 80.8860101631505

x21 = -13.3617694445433

x22 = 62.0364542416117

x23 = -87.1691954703301

x24 = 5.48778647699544

x25 = -101.326363745058

x26 = 51.0608812876208

x27 = 74.6028248559709

x28 = 88.7599931306983

x29 = 18.0541570913546

x30 = 76.1936225163392

x31 = 68.3196395487913

x32 = 57.3440665948004

x33 = -99.7355660846892

x34 = -11.770971784175

x35 = 19.6449547517229

x36 = -88.7599931306983

x37 = 69.9104372091596

x38 = -93.4523807775097

x39 = -36.9037130128934

x40 = 7088.22842532876

x41 = 82.4768078235188

x42 = -38.4945106732617

x43 = 13.3617694445433

x44 = 55.7532689344321

x45 = -30.6205277057138

x46 = -32.2113253660821

x47 = -62.0364542416117

x48 = -49.4700836272525

x49 = -25.9281400589025

x50 = 38.4945106732617

x51 = 93.4523807775097

x52 = 63.62725190198

x53 = -1967.43239997739

x54 = -95.0431784378779

x55 = -19.6449547517229

x56 = 44.7776959804413

x57 = -63.62725190198

x58 = -5.48778647699544

x59 = 95.0431784378779

x60 = 7.07858413736373

x61 = -43.186898320073

x62 = 25.9281400589025

x63 = -18.0541570913546

x64 = -51.0608812876208

x65 = 30.6205277057138

x66 = -82.4768078235188

x67 = 87.1691954703301

x68 = 43.186898320073

График