cos(2x)=-sin(2x) (уравнение)

Найду корень уравнения: cos(2x)=-sin(2x)

Вы ввели

cos(2*x) = -sin(2*x)

$$\cos{\left(2 x \right)} = - \sin{\left(2 x \right)}$$

Подробное решение

Дано уравнение
$$\cos{\left(2 x \right)} = - \sin{\left(2 x \right)}$$
преобразуем:
$$\frac{\sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} = -1$$
или
$$\tan{\left(2 x \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$2 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Или
$$2 x = \pi n + \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$2$$
получим ответ:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$

Быстрый ответ

     -pi 
x1 = ----
      8  

$$x_{1} = - \frac{\pi}{8}$$

Сумма и произведение корней

сумма

    pi
0 - --
    8 

$$- \frac{\pi}{8} + 0$$

=

-pi 
----
 8  

$$- \frac{\pi}{8}$$

произведение

  -pi 
1*----
   8  

$$1 \left(- \frac{\pi}{8}\right)$$

=

-pi 
----
 8  

$$- \frac{\pi}{8}$$

Численный ответ

x1 = 64.009950316892

x2 = 35.7356164345839

x3 = 92.2842841992002

x4 = 87.5718952188155

x5 = -17.6714586764426

x6 = -38.0918109247762

x7 = 40.4480054149686

x8 = 12.1736715326604

x9 = -61.6537558266997

x10 = 71.8639319508665

x11 = -3.53429173528852

x12 = -52.2289778659303

x13 = 79.717913584841

x14 = 56.1559686829176

x15 = -83.6449044018282

x16 = -31.8086256175967

x17 = 26.3108384738145

x18 = -0.392699081698724

x19 = -74.2201264410589

x20 = -30.2378292908018

x21 = -33.3794219443916

x22 = -88.3572933822129

x23 = -55.3705705195201

x24 = 46.7311907221482

x25 = -8.24668071567321

x26 = -80.5033117482384

x27 = -1.96349540849362

x28 = 49.872783375738

x29 = 21.5984494934298

x30 = 62.4391539900971

x31 = 20.0276531666349

x32 = -36.5210145979813

x33 = -41.233403578366

x34 = 100.138265833175

x35 = 48.3019870489431

x36 = 76.5763209312512

x37 = 2.74889357189107

x38 = -96.2112750161874

x39 = 98.5674695063798

x40 = 70.2931356240716

x41 = -89.9280897090078

x42 = 65.5807466436869

x43 = 57.7267650097125

x44 = 93.8550805259951

x45 = 10.6028752058656

x46 = -184.175869316702

x47 = 78.1471172580461

x48 = 4.31968989868597

x49 = -47.5165888855456

x50 = -22.3838476568273

x51 = 9.03207887907065

x52 = 5.89048622548086

x53 = 68.7223392972767

x54 = 54.5851723561227

x55 = -99.3528676697772

x56 = 84.4303025652257

x57 = -25.5254403104171

x58 = -16.1006623496477

x59 = 13.7444678594553

x60 = -75.7909227678538

x61 = -45.9457925587507

x62 = 18993.6764845222

x63 = -66.3661448070844

x64 = -77.3617190946487

x65 = 24.7400421470196

x66 = 43.5895980685584

x67 = -97.7820713429823

x68 = 18.45685683984

x69 = -44.3749962319558

x70 = 42.0188017417635

x71 = -91.4988860358027

x72 = -82.0741080750334

x73 = -69.5077374606742

x74 = 27.8816348006094

x75 = -19.2422550032375

x76 = -9.8174770424681

x77 = 34.164820107789

x78 = 32.5940237809941

x79 = 90.7134878724053

x80 = -60.0829594999048

x81 = -67.9369411338793

x82 = -23.9546439836222

x83 = -39.6626072515711

x84 = -58.5121631731099

x85 = -11.388273369263

x86 = 86.0010988920206

x87 = -53.7997741927252

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