cos(x)=3/5 (уравнение)

Найду корень уравнения: cos(x)=3/5

Вы ввели

cos(x) = 3/5

$$\cos{\left(x \right)} = \frac{3}{5}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{3}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{5} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{5} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{5} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(3/5) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{3}{5} \right)} + 2 \pi$$

x2 = acos(3/5)

$$x_{2} = \operatorname{acos}{\left(\frac{3}{5} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(3/5) + 2*pi + acos(3/5)

$$\operatorname{acos}{\left(\frac{3}{5} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{3}{5} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(3/5) + 2*pi)*acos(3/5)

$$1 \left(- \operatorname{acos}{\left(\frac{3}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{5} \right)}$$

=

(-acos(3/5) + 2*pi)*acos(3/5)

$$\left(- \operatorname{acos}{\left(\frac{3}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{5} \right)}$$

Численный ответ

x1 = -93.3204843896922

x2 = 87.0372990825126

x3 = -68.1877431609738

x4 = 24.2054460107167

x5 = 11.6390753963576

x6 = -30.4886313178963

x7 = 80.754113775333

x8 = 74.4709284681534

x9 = -0.927295218001612

x10 = -55.6213725466147

x11 = -87.0372990825126

x12 = -99.6036696968718

x13 = -43.0550019322555

x14 = 93.3204843896922

x15 = 61.9045578537943

x16 = -44.9095923682587

x17 = -63.7591482897975

x18 = -80.754113775333

x19 = -95.1750748256954

x20 = 51.1927776754383

x21 = -162.435522768668

x22 = 32.3432217538995

x23 = 99.6036696968718

x24 = -5.35589008917797

x25 = -11.6390753963576

x26 = -36.7718166250759

x27 = -26.06003644672

x28 = 43.0550019322555

x29 = 7.2104805251812

x30 = 55.6213725466147

x31 = -49.3381872394351

x32 = -82.6087042113362

x33 = -101.458260132875

x34 = -24.2054460107167

x35 = 13.4936658323608

x36 = 88.8918895185158

x37 = -7.2104805251812

x38 = 49.3381872394351

x39 = 57.4759629826179

x40 = -17.9222607035371

x41 = 0.927295218001612

x42 = 44.9095923682587

x43 = 70.0423335969771

x44 = -51.1927776754383

x45 = -32.3432217538995

x46 = 68.1877431609738

x47 = 17.9222607035371

x48 = 95.1750748256954

x49 = 26.06003644672

x50 = -57.4759629826179

x51 = 76.3255189041567

x52 = 63.7591482897975

x53 = 30.4886313178963

x54 = 19.7768511395404

x55 = 82.6087042113362

x56 = -38.6264070610791

x57 = 38.6264070610791

x58 = -19.7768511395404

x59 = 36.7718166250759

x60 = 5.35589008917797

x61 = -74.4709284681534

x62 = -70.0423335969771

x63 = -61.9045578537943

x64 = -76.3255189041567

x65 = -13.4936658323608

x66 = -88.8918895185158

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