cos(x)=5/13 (уравнение)

Найду корень уравнения: cos(x)=5/13

Вы ввели

cos(x) = 5/13

$$\cos{\left(x \right)} = \frac{5}{13}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{5}{13}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{5}{13} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{5}{13} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{5}{13} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{5}{13} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(5/13) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{5}{13} \right)} + 2 \pi$$

x2 = acos(5/13)

$$x_{2} = \operatorname{acos}{\left(\frac{5}{13} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(5/13) + 2*pi + acos(5/13)

$$\operatorname{acos}{\left(\frac{5}{13} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{5}{13} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(5/13) + 2*pi)*acos(5/13)

$$1 \left(- \operatorname{acos}{\left(\frac{5}{13} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{5}{13} \right)}$$

=

(-acos(5/13) + 2*pi)*acos(5/13)

$$\left(- \operatorname{acos}{\left(\frac{5}{13} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{5}{13} \right)}$$

Численный ответ

x1 = -64.007858278891

x2 = 49.0894772503416

x3 = 23.9567360216232

x4 = -26.3087464358135

x5 = 36.5231066359824

x6 = -11.390365407264

x7 = 95.4237848147889

x8 = 70.2910435860706

x9 = -82.8574142004298

x10 = 74.2222184790599

x11 = -281.567333615986

x12 = 7.45919051427472

x13 = -61.6558478647007

x14 = 57.7246729717114

x15 = -67.9390331718803

x16 = -30.2399213288028

x17 = -86.7885890934191

x18 = -70.2910435860706

x19 = -49.0894772503416

x20 = 61.6558478647007

x21 = 11.390365407264

x22 = -23.9567360216232

x23 = 17.6735507144436

x24 = 67.9390331718803

x25 = 30.2399213288028

x26 = 20.0255611286339

x27 = -17.6735507144436

x28 = -13.7423758214543

x29 = -74.2222184790599

x30 = 42.806291943162

x31 = 51.4414876645318

x32 = 45.1583023573522

x33 = 99.3549597077782

x34 = 82.8574142004298

x35 = 38.8751170501727

x36 = -76.5742288932502

x37 = 5.10718010008445

x38 = -89.1405995076094

x39 = 26.3087464358135

x40 = 64.007858278891

x41 = -93.0717744005987

x42 = -5.10718010008445

x43 = -36.5231066359824

x44 = -7.45919051427472

x45 = 86.7885890934191

x46 = -1.17600520709514

x47 = 32.5919317429931

x48 = -99.3549597077782

x49 = -55.3726625575211

x50 = 1.17600520709514

x51 = 89.1405995076094

x52 = -51.4414876645318

x53 = -38.8751170501727

x54 = -57.7246729717114

x55 = -95.4237848147889

x56 = 55.3726625575211

x57 = -42.806291943162

x58 = -80.5054037862395

x59 = 13.7423758214543

x60 = -32.5919317429931

x61 = 80.5054037862395

x62 = -45.1583023573522

x63 = 93.0717744005987

x64 = -20.0255611286339

x65 = 76.5742288932502

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