cosx=1/4 (уравнение)

Найду корень уравнения: cosx=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

Быстрый ответ

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

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

x2 = acos(1/4)

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

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)

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

Численный ответ

x1 = -92.929663536041

x2 = -67.7969223073226

x3 = 26.4508573003712

x4 = 89.282710372167

x5 = -61.513737000143

x6 = -4.96506923552677

x7 = -23.8146251570655

x8 = -20.1676719931916

x9 = 95.5658956793466

x10 = 55.2305516929635

x11 = 51.5835985290895

x12 = 20.1676719931916

x13 = 99.2128488432206

x14 = -189.81367528704

x15 = -42.6641810786043

x16 = -1421.31799549424

x17 = 61.513737000143

x18 = -30.0978104642451

x19 = -36.3809957714247

x20 = 70.4331544506283

x21 = 57.8667838362691

x22 = 11.2482545427064

x23 = -48.9473663857839

x24 = 42.6641810786043

x25 = 82.9995250649874

x26 = -55.2305516929635

x27 = 30.0978104642451

x28 = -1.31811607165282

x29 = 1.31811607165282

x30 = 7.6013013788324

x31 = 39.0172279147303

x32 = -89.282710372167

x33 = 4.96506923552677

x34 = 48.9473663857839

x35 = -99.2128488432206

x36 = -13.884486686012

x37 = 86.6464782288614

x38 = 80.3632929216818

x39 = -74.0801076145022

x40 = -76.7163397578079

x41 = -95.5658956793466

x42 = 17.5314398498859

x43 = 36.3809957714247

x44 = -57.8667838362691

x45 = -39.0172279147303

x46 = 23.8146251570655

x47 = -17.5314398498859

x48 = -26.4508573003712

x49 = 74.0801076145022

x50 = 64.1499691434487

x51 = -82.9995250649874

x52 = -64.1499691434487

x53 = -70.4331544506283

x54 = -51.5835985290895

x55 = -80.3632929216818

x56 = -86.6464782288614

x57 = -7.6013013788324

x58 = 13.884486686012

x59 = 67.7969223073226

x60 = 45.3004132219099

x61 = -11.2482545427064

x62 = -32.7340426075507

x63 = 92.929663536041

x64 = -45.3004132219099

x65 = 32.7340426075507

x66 = 76.7163397578079

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