cos(4x)=√3/2 (уравнение)

Найду корень уравнения: cos(4x)=√3/2

Вы ввели

             ___
           \/ 3 
cos(4*x) = -----
             2  

$$\cos{\left(4 x \right)} = \frac{\sqrt{3}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(4 x \right)} = \frac{\sqrt{3}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$4 x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$4 x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{3}}{2} \right)}$$
Или
$$4 x = \pi n + \frac{\pi}{6}$$
$$4 x = \pi n - \frac{5 \pi}{6}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$4$$
получим ответ:
$$x_{1} = \frac{\pi n}{4} + \frac{\pi}{24}$$
$$x_{2} = \frac{\pi n}{4} - \frac{5 \pi}{24}$$

Быстрый ответ

     pi
x1 = --
     24

$$x_{1} = \frac{\pi}{24}$$

     11*pi
x2 = -----
       24 

$$x_{2} = \frac{11 \pi}{24}$$

Численный ответ

x1 = -11350.7051571138

x2 = 72.1257313386657

x3 = 95.9494756283883

x4 = 89.6662903212087

x5 = 14.2680666350536

x6 = -89.6662903212087

x7 = -75.5291233800546

x8 = -83.1213056262299

x9 = 100.400065220974

x10 = -35.997415822383

x11 = 42.2806011295626

x12 = -7.72308194007491

x13 = 51.9671784781312

x14 = 80.2415123604393

x15 = -45.6839931709516

x16 = 88.0954939944138

x17 = -53.5379748049261

x18 = -81.8123086872342

x19 = 34.4266194955881

x20 = 70.5549350118708

x21 = -100.661864608773

x22 = 0.130899693899575

x23 = 81.8123086872342

x24 = 64.2717497046912

x25 = -67.6751417460801

x26 = -15.8388629618485

x27 = 45.6839931709516

x28 = 4.58148928648512

x29 = -9.55567765466895

x30 = -22.1220482690281

x31 = 22.1220482690281

x32 = 36.2592152101822

x33 = -17.4096592886434

x34 = 35.997415822383

x35 = -6.15228561328001

x36 = 66.1043454192852

x37 = 26.8344372494128

x38 = -65.8425460314861

x39 = -39.400807863772

x40 = -43.8513974563575

x41 = -31.5468262297975

x42 = 28.1434341884086

x43 = -37.8300115369771

x44 = -56.6795674585159

x45 = -59.8211601121056

x46 = -20.2894525544341

x47 = 6.15228561328001

x48 = -78.6707160336444

x49 = 29.9760299030026

x50 = -79.9797129726402

x51 = -1.70169602069447

x52 = 59.8211601121056

x53 = -94.1168799137942

x54 = 67.6751417460801

x55 = 12.4354709204596

x56 = 92.5460835869993

x57 = 78.4089166458453

x58 = -29.7142305152035

x59 = 15.8388629618485

x60 = 18.7186562276392

x61 = -72.1257313386657

x62 = -28.1434341884086

x63 = -57.9885643975116

x64 = 102.232660935568

x65 = -64.2717497046912

x66 = 48.5637864367422

x67 = 73.9583270532597

x68 = -14.0062672472545

x69 = -73.6965276654606

x70 = 50.1345827635371

x71 = 86.2628982798197

x72 = -97.5202719551832

x73 = 37.8300115369771

x74 = 55.108771131721

x75 = -21.860248881229

x76 = 20.2894525544341

x77 = 58.2503637853107

x78 = 56.4177680707167

x79 = -84.953901340824

x80 = -86.2628982798197

x81 = 7.98488132787406

x82 = -23.692844595823

x83 = -42.2806011295626

x84 = 23.692844595823

x85 = -50.1345827635371

x86 = 26.5726378616137

x87 = -95.6876762405891

x88 = 1.70169602069447

x89 = 94.1168799137942

x90 = 44.1131968441567

x91 = -51.705379090332

x92 = -87.8336946066146

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