cos(x)=-0,75 (уравнение)

Найду корень уравнения: cos(x)=-0,75

Вы ввели

cos(x) = -3/4

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

Подробное решение

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

Быстрый ответ

x1 = -acos(-3/4) + 2*pi

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

x2 = acos(-3/4)

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

Сумма и произведение корней

сумма

0 + -acos(-3/4) + 2*pi + acos(-3/4)

$$\operatorname{acos}{\left(- \frac{3}{4} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{3}{4} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-3/4) + 2*pi)*acos(-3/4)

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

=

(-acos(-3/4) + 2*pi)*acos(-3/4)

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

Численный ответ

x1 = -16.4306975157624

x2 = -21.2684143273151

x3 = 2.41885840577638

x4 = -14.9852290201356

x5 = 33.8347849416743

x6 = -28.9970681301216

x7 = -52.6843408632131

x8 = 52.6843408632131

x9 = -85.5457358947378

x10 = 98.112106509097

x11 = -27.5515996344947

x12 = 123.244847737815

x13 = -3.86432690140321

x14 = 8.70204371295596

x15 = 385.693162143731

x16 = -22.713882822942

x17 = 54.1298093588399

x18 = -79.2625505875583

x19 = -65.2507114775722

x20 = -96.6666380134702

x21 = 41.5634387444807

x22 = -33.8347849416743

x23 = 40.1179702488539

x24 = 84.100267399111

x25 = -54.1298093588399

x26 = 60.4129946660195

x27 = 10.1475122085828

x28 = 14.9852290201356

x29 = 79.2625505875583

x30 = 46.4011555560335

x31 = 90.3834527062906

x32 = -66.6961799731991

x33 = -71.5338967847518

x34 = -2.41885840577638

x35 = -60.4129946660195

x36 = 72.9793652803787

x37 = 58.9675261703927

x38 = -46.4011555560335

x39 = 16.4306975157624

x40 = 105094.976306292

x41 = 77.8170820919314

x42 = 85.5457358947378

x43 = -90.3834527062906

x44 = -77.8170820919314

x45 = -72.9793652803787

x46 = 91.8289212019174

x47 = -8.70204371295596

x48 = -98.112106509097

x49 = 27.5515996344947

x50 = 21.2684143273151

x51 = 28.9970681301216

x52 = 22.713882822942

x53 = 3.86432690140321

x54 = -58.9675261703927

x55 = -47.8466240516603

x56 = 71.5338967847518

x57 = -91.8289212019174

x58 = -40.1179702488539

x59 = -10.1475122085828

x60 = 96.6666380134702

x61 = 65.2507114775722

x62 = -41.5634387444807

x63 = 66.6961799731991

x64 = -35.2802534373011

x65 = 35.2802534373011

x66 = -84.100267399111

x67 = 47.8466240516603

График