cos(4x)=1 (уравнение)

Найду корень уравнения: cos(4x)=1

Вы ввели

cos(4*x) = 1

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

Подробное решение

Дано уравнение
$$\cos{\left(4 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Или
$$4 x = \pi n$$
$$4 x = \pi n - \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4}$$
$$x_{2} = \frac{\pi n}{4} - \frac{\pi}{4}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     pi
x2 = --
     2 

$$x_{2} = \frac{\pi}{2}$$

Сумма и произведение корней

сумма

        pi
0 + 0 + --
        2 

$$\left(0 + 0\right) + \frac{\pi}{2}$$

=

pi
--
2 

$$\frac{\pi}{2}$$

произведение

    pi
1*0*--
    2 

$$1 \cdot 0 \frac{\pi}{2}$$

=

0

$$0$$

Численный ответ

x1 = 37.6991119665793

x2 = 67.5442420634706

x3 = 92.6769832182628

x4 = 95.8185756842062

x5 = -17.2787595621355

x6 = -43.9822971747455

x7 = 94.247779609353

x8 = -23.5619449982306

x9 = -94.247779486083

x10 = -42.4115007432387

x11 = 12.5663704969137

x12 = 87.9645943351391

x13 = -20.4203521774723

x14 = 72.256630710694

x15 = 4.71238898608896

x16 = 26.7035375390573

x17 = -53.4070752253874

x18 = 59.690260541069

x19 = -31.4159266517141

x20 = 43.9822971692691

x21 = 36.1283154718409

x22 = 64.4026493150839

x23 = 70.6858346557926

x24 = 89.5353906153414

x25 = -58.1194640062544

x26 = 42.4115007365289

x27 = -344.004395625893

x28 = 7.85398173011892

x29 = 20.4203521581227

x30 = -6.28318518328035

x31 = 34.5575190717885

x32 = -14.1371668484631

x33 = -89.5353907315491

x34 = 45.5530935075531

x35 = 50.2654824463816

x36 = 51.8362788866811

x37 = -64.402649310466

x38 = 29.8451303084991

x39 = -81.6814090370675

x40 = -67.5442421539445

x41 = -86.3937978789102

x42 = -39.2699081045218

x43 = -73.8274272808521

x44 = -1.57079626356835

x45 = -80.1106125854791

x46 = 21.9911485851564

x47 = 56.5486676469942

x48 = -59.6902604569585

x49 = 14.1371670778185

x50 = 23.5619449483644

x51 = -65.9734457653935

x52 = 48.6946860958663

x53 = 73.8274274646672

x54 = -83.2522051669813

x55 = -95.818575868455

x56 = -29.8451301000724

x57 = -87.9645943594276

x58 = -100.530965206253

x59 = -51.8362786915081

x60 = -97.3893725907902

x61 = 15.7079633917898

x62 = 95.8185760424586

x63 = 1.57079638652515

x64 = 86.3937978937855

x65 = -9.42477807759933

x66 = -75.3982237985682

x67 = 65.9734457525462

x68 = 72.2566310277248

x69 = -97.3893723711949

x70 = -72.2566309100272

x71 = -61.2610566398387

x72 = 81.6814091152362

x73 = 0.0

x74 = -36.128315427252

x75 = 100.530964798296

x76 = -1.57079642013166

x77 = -37.6991118766796

x78 = -15.7079632962205

x79 = -21.9911485864927

x80 = -7.85398150696156

x81 = 117.809724442492

x82 = -28.2743337586152

x83 = -45.5530935761698

x84 = 78.5398162225044

x85 = 6.28318528443138

x86 = 28.2743338652921

x87 = -50.2654823342013

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