cos(x)=-√3/4 (уравнение)

Найду корень уравнения: cos(x)=-√3/4

Вы ввели

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

$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{4}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{\left(-1\right) \sqrt{3}}{4}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{4} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{3}}{4} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{3}}{4} \right)}$$
, где n - любое целое число

Быстрый ответ

           /   ___ \       
           |-\/ 3  |       
x1 = - acos|-------| + 2*pi
           \   4   /       

$$x_{1} = - \operatorname{acos}{\left(- \frac{\sqrt{3}}{4} \right)} + 2 \pi$$

         /   ___ \
         |-\/ 3  |
x2 = acos|-------|
         \   4   /

$$x_{2} = \operatorname{acos}{\left(- \frac{\sqrt{3}}{4} \right)}$$

Численный ответ

x1 = 14.584999338083

x2 = 67.0964096552516

x3 = 64.8504817955197

x4 = 23.1141125049945

x5 = -39.7177405668013

x6 = -79.6627802696108

x7 = -48.2468537337129

x8 = 89.983223024238

x9 = 41.9636684265333

x10 = 48.2468537337129

x11 = 27.1513699524422

x12 = 121.399149560136

x13 = -20.8681846452626

x14 = 60.813224348072

x15 = -41.9636684265333

x16 = -85.9459655767904

x17 = 29.3972978121741

x18 = -58.5672964883401

x19 = -16.8309271978149

x20 = 54.5300390408924

x21 = -83.7000377170584

x22 = 2.01862872372383

x23 = -8.30181403090342

x24 = -92.22915088397

x25 = -52.2841111811605

x26 = -67.0964096552516

x27 = 96.2664083314176

x28 = 16.8309271978149

x29 = 58.5672964883401

x30 = -35.6804831193537

x31 = 4.26455658345576

x32 = -64.8504817955197

x33 = 46.0009258739809

x34 = -96.2664083314176

x35 = -73.3795949624312

x36 = -2.01862872372383

x37 = -46.0009258739809

x38 = -89.983223024238

x39 = 77.4168524098789

x40 = -27.1513699524422

x41 = 98.5123361911496

x42 = -14.584999338083

x43 = -10.5477418906353

x44 = -98.5123361911496

x45 = -77.4168524098789

x46 = 71.1336671026993

x47 = -29.3972978121741

x48 = -54.5300390408924

x49 = -4.26455658345576

x50 = 52.2841111811605

x51 = 85.9459655767904

x52 = -33.4345552596218

x53 = 83.7000377170584

x54 = 39.7177405668013

x55 = 92.22915088397

x56 = -71.1336671026993

x57 = 35.6804831193537

x58 = 10.5477418906353

x59 = 79.6627802696108

x60 = 8.30181403090342

x61 = 73.3795949624312

x62 = -60.813224348072

x63 = 20.8681846452626

x64 = -23.1141125049945

x65 = 33.4345552596218

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