cosx=cos3 (уравнение)

Найду корень уравнения: cosx=cos3

Вы ввели

cos(x) = cos(3)

$$\cos{\left(x \right)} = \cos{\left(3 \right)}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \cos{\left(3 \right)}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\cos{\left(3 \right)} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\cos{\left(3 \right)} \right)}$$
Или
$$x = \pi n + 3$$
$$x = \pi n - \pi + 3$$
, где n - любое целое число

Быстрый ответ

x1 = 3

$$x_{1} = 3$$

x2 = -3 + 2*pi

$$x_{2} = -3 + 2 \pi$$

Сумма и произведение корней

сумма

3 + -3 + 2*pi

$$3 + \left(-3 + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

3*(-3 + 2*pi)

$$3 \left(-3 + 2 \pi\right)$$

=

-9 + 6*pi

$$-9 + 6 \pi$$

Численный ответ

x1 = -59.5486677646163

x2 = -477531.649716263

x3 = 72.398223686155

x4 = -65.8318530717959

x5 = 97.2477796076938

x6 = -53.2654824574367

x7 = -91.2477796076938

x8 = 40.6991118430775

x9 = 40.9822971502571

x10 = 90.9645943005142

x11 = -46.9822971502571

x12 = 47.2654824574367

x13 = -34.6991118430775

x14 = -78.398223686155

x15 = 22.1327412287183

x16 = -28.4159265358979

x17 = -72.1150383789755

x18 = 97.5309649148734

x19 = 91.2477796076938

x20 = 59.8318530717959

x21 = -40.6991118430775

x22 = 9.28318530717959

x23 = 3.0

x24 = -172.929188601028

x25 = -3653.81384877852

x26 = 69331.9498647267

x27 = -53.5486677646163

x28 = -84.6814089933346

x29 = 78.6814089933346

x30 = -40.9822971502571

x31 = 84.9645943005142

x32 = -97.2477796076938

x33 = -22.1327412287183

x34 = -28.1327412287183

x35 = -59.8318530717959

x36 = 15.5663706143592

x37 = -66.1150383789755

x38 = 46.9822971502571

x39 = 78.398223686155

x40 = -47.2654824574367

x41 = 28.1327412287183

x42 = -90.9645943005142

x43 = -9.28318530717959

x44 = 9.56637061435917

x45 = -3.28318530717959

x46 = 28.4159265358979

x47 = -34.4159265358979

x48 = -15.5663706143592

x49 = -84.9645943005142

x50 = -21.8495559215388

x51 = 21.8495559215388

x52 = -3.0

x53 = -78.6814089933346

x54 = 72.1150383789755

x55 = 53.2654824574367

x56 = -15.8495559215388

x57 = 84.6814089933346

x58 = -2032.46885421901

x59 = -97.5309649148734

x60 = -72.398223686155

x61 = 15.8495559215388

x62 = 34.6991118430775

x63 = 59.5486677646163

x64 = 53.5486677646163

x65 = 34.4159265358979

x66 = 3.28318530717959

x67 = 66.1150383789755

x68 = 65.8318530717959

x69 = -9.56637061435917

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