cos(x)=1/4 (уравнение)

Найду корень уравнения: cos(x)=1/4

Вы ввели

cos(x) = 1/4

$$\cos{\left(x \right)} = \frac{1}{4}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{1}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{1}{4} \right)}$$
, где n - любое целое число

Сумма и произведение корней

сумма

0 + -acos(1/4) + 2*pi + acos(1/4)

$$\operatorname{acos}{\left(\frac{1}{4} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(1/4) + 2*pi)*acos(1/4)

$$1 \left(- \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{4} \right)}$$

=

(-acos(1/4) + 2*pi)*acos(1/4)

$$\left(- \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{1}{4} \right)}$$

Быстрый ответ

x1 = -acos(1/4) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(\frac{1}{4} \right)} + 2 \pi$$

x2 = acos(1/4)

$$x_{2} = \operatorname{acos}{\left(\frac{1}{4} \right)}$$

Численный ответ

x1 = -17.5314398498859

x2 = 92.929663536041

x3 = 11.2482545427064

x4 = 51.5835985290895

x5 = -99.2128488432206

x6 = 17.5314398498859

x7 = 67.7969223073226

x8 = -48.9473663857839

x9 = 89.282710372167

x10 = -76.7163397578079

x11 = 61.513737000143

x12 = 95.5658956793466

x13 = -95.5658956793466

x14 = -42.6641810786043

x15 = 30.0978104642451

x16 = 57.8667838362691

x17 = 36.3809957714247

x18 = 32.7340426075507

x19 = -23.8146251570655

x20 = -30.0978104642451

x21 = -39.0172279147303

x22 = -20.1676719931916

x23 = -64.1499691434487

x24 = 39.0172279147303

x25 = 1.31811607165282

x26 = -45.3004132219099

x27 = -189.81367528704

x28 = 80.3632929216818

x29 = 23.8146251570655

x30 = -32.7340426075507

x31 = -82.9995250649874

x32 = 99.2128488432206

x33 = -55.2305516929635

x34 = -70.4331544506283

x35 = 48.9473663857839

x36 = 42.6641810786043

x37 = 20.1676719931916

x38 = 64.1499691434487

x39 = -1421.31799549424

x40 = 82.9995250649874

x41 = -51.5835985290895

x42 = -4.96506923552677

x43 = 70.4331544506283

x44 = 76.7163397578079

x45 = -86.6464782288614

x46 = 55.2305516929635

x47 = -67.7969223073226

x48 = 7.6013013788324

x49 = -61.513737000143

x50 = 45.3004132219099

x51 = -36.3809957714247

x52 = -74.0801076145022

x53 = -7.6013013788324

x54 = 86.6464782288614

x55 = -26.4508573003712

x56 = -1.31811607165282

x57 = 4.96506923552677

x58 = 13.884486686012

x59 = -80.3632929216818

x60 = -89.282710372167

x61 = 74.0801076145022

x62 = 26.4508573003712

x63 = -11.2482545427064

x64 = -13.884486686012

x65 = -57.8667838362691

x66 = -92.929663536041

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