cos(pi/2*(x-2))=0 (уравнение)

Найду корень уравнения: cos(pi/2*(x-2))=0

Вы ввели

   /pi        \    
cos|--*(x - 2)| = 0
   \2         /    

$$\cos{\left(\frac{\pi}{2} \left(x - 2\right) \right)} = 0$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{\pi}{2} \left(x - 2\right) \right)} = 0$$
- это простейшее тригонометрическое ур-ние

с изменением знака при 0

Получим:
$$\cos{\left(\frac{\pi}{2} \left(x - 2\right) \right)} = 0$$

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\cos{\left(\frac{\pi x}{2} \right)} = 0$$
Это ур-ние преобразуется в
$$\frac{\pi x}{2} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$\frac{\pi x}{2} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Или
$$\frac{\pi x}{2} = \pi n + \frac{\pi}{2}$$
$$\frac{\pi x}{2} = \pi n - \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{\pi}{2}$$
получим ответ:
$$x_{1} = \frac{2 \left(\pi n + \frac{\pi}{2}\right)}{\pi}$$
$$x_{2} = \frac{2 \left(\pi n - \frac{\pi}{2}\right)}{\pi}$$

Быстрый ответ

x1 = 1

$$x_{1} = 1$$

x2 = 3

$$x_{2} = 3$$

Сумма и произведение корней

сумма

1 + 3

$$1 + 3$$

=

4

$$4$$

произведение

3

$$3$$

=

3

$$3$$

Численный ответ

x1 = 105.0

x2 = 59.0

x3 = -47.0

x4 = -21.0

x5 = 29.0

x6 = -19.0

x7 = -9.0

x8 = -91.0

x9 = 65.0

x10 = 35.0

x11 = -7.0

x12 = -3.0

x13 = 21.0

x14 = -33.0

x15 = 39.0

x16 = 7.0

x17 = 103.0

x18 = -39.0

x19 = 57.0

x20 = 17.0

x21 = -89.0

x22 = 61.0

x23 = -61.0

x24 = 71.0

x25 = -69.0

x26 = 93.0

x27 = -43.0

x28 = -13.0

x29 = -71.0

x30 = 67.0

x31 = 77.0

x32 = 75.0

x33 = 41.0

x34 = -79.0

x35 = -81.0

x36 = 3.0

x37 = 55.0

x38 = -93.0

x39 = 73.0

x40 = -37.0

x41 = 49.0

x42 = -49.0

x43 = -87.0

x44 = 37.0

x45 = -75.0

x46 = -35.0

x47 = 91.0

x48 = 5.0

x49 = 99.0

x50 = -85.0

x51 = 47.0

x52 = 9.0

x53 = 87.0

x54 = 97.0

x55 = -15.0

x56 = -25.0

x57 = 31.0

x58 = 79.0

x59 = -53.0

x60 = 89.0

x61 = 45.0

x62 = -65.0

x63 = -73.0

x64 = 1.0

x65 = 63.0

x66 = -31.0

x67 = 95.0

x68 = 51.0

x69 = 43.0

x70 = -41.0

x71 = -5.0

x72 = 15.0

x73 = -77.0

x74 = -83.0

x75 = 27.0

x76 = -59.0

x77 = -1.0

x78 = -11.0

x79 = -27.0

x80 = 25.0

x81 = 33.0

x82 = 11.0

x83 = 23.0

x84 = -51.0

x85 = 13.0

x86 = -29.0

x87 = 81.0

x88 = -23.0

x89 = -55.0

x90 = 85.0

x91 = 19.0

x92 = 101.0

x93 = -17.0

x94 = 53.0

x95 = -95.0

x96 = 69.0

x97 = -63.0

x98 = -57.0

x99 = -45.0

x100 = -67.0

x101 = 83.0

График