cos(x)=-(3/8) (уравнение)

Найду корень уравнения: cos(x)=-(3/8)

Вы ввели

cos(x) = -3/8

$$\cos{\left(x \right)} = - \frac{3}{8}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{3}{8}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{8} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{3}{8} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{3}{8} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-3/8) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{3}{8} \right)} + 2 \pi$$

x2 = acos(-3/8)

$$x_{2} = \operatorname{acos}{\left(- \frac{3}{8} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-3/8) + 2*pi + acos(-3/8)

$$\operatorname{acos}{\left(- \frac{3}{8} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{3}{8} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-3/8) + 2*pi)*acos(-3/8)

$$1 \left(- \operatorname{acos}{\left(- \frac{3}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{3}{8} \right)}$$

=

(-acos(-3/8) + 2*pi)*acos(-3/8)

$$\left(- \operatorname{acos}{\left(- \frac{3}{8} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{3}{8} \right)}$$

Численный ответ

x1 = -29.4607334346074

x2 = 58.5038608659068

x3 = 79.7262158920441

x4 = -77.3534167874456

x5 = -79.7262158920441

x6 = -48.3102893561462

x7 = -16.8943628202482

x8 = -86.0094011992237

x9 = 27.0879343300089

x10 = -98.5757718135828

x11 = 23.1775481274278

x12 = 35.743918741787

x13 = 92.2925865064033

x14 = 29.4607334346074

x15 = 77.3534167874456

x16 = 71.070231480266

x17 = 4.32799220588905

x18 = 96.2029727089843

x19 = -92.2925865064033

x20 = 98.5757718135828

x21 = -23.1775481274278

x22 = -4.32799220588905

x23 = -1.95519310129054

x24 = 60.8766599705053

x25 = -64.7870461730864

x26 = 39.6543049443681

x27 = -10.6111775130686

x28 = -89.9197874018047

x29 = 1.95519310129054

x30 = -83.6366020946252

x31 = -54.5934746633257

x32 = -58.5038608659068

x33 = -39.6543049443681

x34 = -96.2029727089843

x35 = 16.8943628202482

x36 = 20.8047490228293

x37 = 54.5934746633257

x38 = -52.2206755587272

x39 = 83.6366020946252

x40 = 86.0094011992237

x41 = -33.3711196371885

x42 = 8.23837840847012

x43 = -73.4430305848645

x44 = 67.1598452776849

x45 = 48.3102893561462

x46 = -42.0271040489666

x47 = -20.8047490228293

x48 = -45.9374902515476

x49 = 64.7870461730864

x50 = -14.5215637156497

x51 = -27.0879343300089

x52 = -35.743918741787

x53 = 10.6111775130686

x54 = 14.5215637156497

x55 = -8.23837840847012

x56 = -67.1598452776849

x57 = 73.4430305848645

x58 = -71.070231480266

x59 = 89.9197874018047

x60 = 33.3711196371885

x61 = 52.2206755587272

x62 = -60.8766599705053

x63 = 42.0271040489666

x64 = 45.9374902515476

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