6cosx=5 (уравнение)

Найду корень уравнения: 6cosx=5

Вы ввели

6*cos(x) = 5

$$6 \cos{\left(x \right)} = 5$$

Подробное решение

Дано уравнение
$$6 \cos{\left(x \right)} = 5$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на 6

Ур-ние превратится в
$$\cos{\left(x \right)} = \frac{5}{6}$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{5}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{5}{6} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{5}{6} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{5}{6} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(5/6) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{5}{6} \right)} + 2 \pi$$

x2 = acos(5/6)

$$x_{2} = \operatorname{acos}{\left(\frac{5}{6} \right)}$$

Сумма и произведение корней

сумма

-acos(5/6) + 2*pi + acos(5/6)

$$\operatorname{acos}{\left(\frac{5}{6} \right)} + \left(- \operatorname{acos}{\left(\frac{5}{6} \right)} + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

(-acos(5/6) + 2*pi)*acos(5/6)

$$\left(- \operatorname{acos}{\left(\frac{5}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{5}{6} \right)}$$

=

(-acos(5/6) + 2*pi)*acos(5/6)

$$\left(- \operatorname{acos}{\left(\frac{5}{6} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{5}{6} \right)}$$

Численный ответ

x1 = 82.2670945367918

x2 = 57.1343533080734

x3 = -69.7007239224326

x4 = 68.5293528355183

x5 = -30.8302409924408

x6 = -68.5293528355183

x7 = -93.6620940642366

x8 = -24.5470556852612

x9 = -13.1520561578163

x10 = 74.8125381426979

x11 = -75.9839092296122

x12 = -50.8511680008938

x13 = 0.585685543457151

x14 = -5.69749976372244

x15 = 30.8302409924408

x16 = -63.417538615253

x17 = -49.6797969139795

x18 = 13.1520561578163

x19 = -37.1134262996204

x20 = -55.9629822211591

x21 = 32.0016120793551

x22 = 93.6620940642366

x23 = 49.6797969139795

x24 = -6.86887085063674

x25 = 63.417538615253

x26 = -94.8334651511509

x27 = 44.5679826937143

x28 = -11.980685070902

x29 = 6.86887085063674

x30 = 88.5502798439714

x31 = -82.2670945367918

x32 = 18.2638703780816

x33 = -62.2461675283387

x34 = 11.980685070902

x35 = -74.8125381426979

x36 = 50.8511680008938

x37 = -19.4352414649959

x38 = 25.7184267721755

x39 = -32.0016120793551

x40 = 55.9629822211591

x41 = -49650.3159828765

x42 = 81.0957234498775

x43 = 19.4352414649959

x44 = -101.116650458331

x45 = -81.0957234498775

x46 = 62.2461675283387

x47 = 87.3789087570571

x48 = -57.1343533080734

x49 = 37.1134262996204

x50 = 99.9452793714162

x51 = -25.7184267721755

x52 = -99.9452793714162

x53 = 38.2847973865347

x54 = 43.3966116068

x55 = 24.5470556852612

x56 = -43.3966116068

x57 = 5.69749976372244

x58 = 75.9839092296122

x59 = -18.2638703780816

x60 = -87.3789087570571

x61 = 69.7007239224326

x62 = -38.2847973865347

x63 = -0.585685543457151

x64 = 94.8334651511509

x65 = -44.5679826937143

x66 = -88.5502798439714

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