(cos(x)-sin(x))=0 (уравнение)

Найду корень уравнения: (cos(x)-sin(x))=0

Вы ввели

cos(x) - sin(x) = 0

$$- \sin{\left (x \right )} + \cos{\left (x \right )} = 0$$

Подробное решение

Дано уравнение
$$- \sin{\left (x \right )} + \cos{\left (x \right )} = 0$$
преобразуем:
$$- \frac{\sin{\left (x \right )}}{\cos{\left (x \right )}} = -1$$
или
$$- \tan{\left (x \right )} = -1$$
- это простейшее тригонометрическое ур-ние

Разделим обе части ур-ния на -1

Ур-ние превратится в
$$\tan{\left (x \right )} = -1$$
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{atan}{\left (-1 \right )}$$
Или
$$x = \pi n - \frac{\pi}{4}$$
, где n - любое целое число

Быстрый ответ

     -3*pi
x1 = -----
       4  

$$x_{1} = - \frac{3 \pi}{4}$$

     pi
x2 = --
     4 

$$x_{2} = \frac{\pi}{4}$$

Численный ответ

x1 = -80.8960108299000

x2 = 73.0420291960000

x3 = 101.316363078000

x4 = -77.7544181763000

x5 = -33.7721210261000

x6 = -8.63937979737000

x7 = 82.4668071567000

x8 = 10.2101761242000

x9 = 0.785398163397000

x10 = 85.6083998103000

x11 = 22.7765467385000

x12 = 32.2013246993000

x13 = 51.0508806208000

x14 = 25.9181393921000

x15 = -5.49778714378000

x16 = 57.3340659280000

x17 = -43.1968989869000

x18 = 29.0597320457000

x19 = -27.4889357189000

x20 = 91.8915851175000

x21 = -99.7455667515000

x22 = 1672.11268987000

x23 = -71.4712328692000

x24 = -2.35619449019000

x25 = -74.6128255228000

x26 = 88.7499924639000

x27 = 76.1836218496000

x28 = 3.92699081699000

x29 = -55.7632696012000

x30 = -40.0553063333000

x31 = -36.9137136797000

x32 = 35.3429173529000

x33 = 79.3252145031000

x34 = -228.550865549000

x35 = 95.0331777711000

x36 = -58.9048622548000

x37 = -46.3384916404000

x38 = 66.7588438888000

x39 = 47.9092879672000

x40 = 69.9004365424000

x41 = 7.06858347058000

x42 = -96.6039740979000

x43 = 13.3517687778000

x44 = 98.1747704247000

x45 = 41.6261026601000

x46 = 63.6172512352000

x47 = 60.4756585816000

x48 = 16.4933614313000

x49 = 19.6349540849000

x50 = 38.4845100065000

x51 = -18.0641577581000

x52 = -21.2057504117000

x53 = -62.0464549084000

x54 = -49.4800842940000

x55 = -84.0376034835000

x56 = -52.6216769476000

x57 = -68.3296402156000

x58 = -93.4623814443000

x59 = 44.7676953137000

x60 = -87.1791961371000

x61 = -24.3473430653000

x62 = -14.9225651046000

x63 = -11.7809724510000

x64 = -90.3207887907000

x65 = 54.1924732744000

x66 = -30.6305283725000

x67 = -65.1880475620000

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