cos(x)=-1/7 (уравнение)

Найду корень уравнения: cos(x)=-1/7

Вы ввели

cos(x) = -1/7

$$\cos{\left(x \right)} = - \frac{1}{7}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = - \frac{1}{7}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{7} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(- \frac{1}{7} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{7} \right)}$$
, где n - любое целое число

Быстрый ответ

x1 = -acos(-1/7) + 2*pi

$$x_{1} = - \operatorname{acos}{\left(- \frac{1}{7} \right)} + 2 \pi$$

x2 = acos(-1/7)

$$x_{2} = \operatorname{acos}{\left(- \frac{1}{7} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(-1/7) + 2*pi + acos(-1/7)

$$\operatorname{acos}{\left(- \frac{1}{7} \right)} + \left(0 + \left(- \operatorname{acos}{\left(- \frac{1}{7} \right)} + 2 \pi\right)\right)$$

=

2*pi

$$2 \pi$$

произведение

1*(-acos(-1/7) + 2*pi)*acos(-1/7)

$$1 \left(- \operatorname{acos}{\left(- \frac{1}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{7} \right)}$$

=

(-acos(-1/7) + 2*pi)*acos(-1/7)

$$\left(- \operatorname{acos}{\left(- \frac{1}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(- \frac{1}{7} \right)}$$

Численный ответ

x1 = 48.5513385617364

x2 = 89.6787381962145

x3 = 98.8168210191731

x4 = 51.979626353137

x5 = 42.2681532545568

x6 = -23.4185973330181

x7 = -17.1354120258385

x8 = 61.1177091760956

x9 = -7.99732920287985

x10 = -86.2504504048139

x11 = -33.1300704315982

x12 = -79.9672650976344

x13 = 26.8468851244186

x14 = 58.2628116603165

x15 = 102.245108810574

x16 = 1.71414389570026

x17 = 33.1300704315982

x18 = 35.9849679473773

x19 = -45.6964410459574

x20 = -61.1177091760956

x21 = 20.563699817239

x22 = -26.8468851244186

x23 = 64.5459969674961

x24 = -70.8291822746757

x25 = -35.9849679473773

x26 = -48.5513385617364

x27 = -51.979626353137

x28 = -39.4132557387778

x29 = 70.8291822746757

x30 = -58.2628116603165

x31 = -67.4008944832752

x32 = -14.2805145100594

x33 = -77.1123675818553

x34 = -331.294677384818

x35 = -29.7017826401977

x36 = 39.4132557387778

x37 = 45.6964410459574

x38 = 92.5336357119935

x39 = -73.6840797904548

x40 = -92.5336357119935

x41 = 86.2504504048139

x42 = -83.3955528890349

x43 = -89.6787381962145

x44 = -64.5459969674961

x45 = 83.3955528890349

x46 = -54.834523868916

x47 = 79.9672650976344

x48 = 73.6840797904548

x49 = 23.4185973330181

x50 = 67.4008944832752

x51 = -10.8522267186589

x52 = -5351.55973782131

x53 = -42.2681532545568

x54 = -98.8168210191731

x55 = -1.71414389570026

x56 = 17.1354120258385

x57 = -95.9619235033941

x58 = 4.56904141147932

x59 = 14.2805145100594

x60 = 10.8522267186589

x61 = -20.563699817239

x62 = 7.99732920287985

x63 = 54.834523868916

x64 = 77.1123675818553

x65 = 95.9619235033941

x66 = -4.56904141147932

x67 = 29.7017826401977

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