cos17x=-√2/2 (уравнение)

Найду корень уравнения: cos17x=-√2/2

Вы ввели

               ___ 
            -\/ 2  
cos(17*x) = -------
               2   

$$\cos{\left(17 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$

Подробное решение

Дано уравнение
$$\cos{\left(17 x \right)} = \frac{\left(-1\right) \sqrt{2}}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$17 x = \pi n + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
$$17 x = \pi n - \pi + \operatorname{acos}{\left(- \frac{\sqrt{2}}{2} \right)}$$
Или
$$17 x = \pi n + \frac{3 \pi}{4}$$
$$17 x = \pi n - \frac{\pi}{4}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$17$$
получим ответ:
$$x_{1} = \frac{\pi n}{17} + \frac{3 \pi}{68}$$
$$x_{2} = \frac{\pi n}{17} - \frac{\pi}{68}$$

Быстрый ответ

     3*pi
x1 = ----
      68 

$$x_{1} = \frac{3 \pi}{68}$$

     5*pi
x2 = ----
      68 

$$x_{2} = \frac{5 \pi}{68}$$

Сумма и произведение корней

сумма

    3*pi   5*pi
0 + ---- + ----
     68     68 

$$\left(0 + \frac{3 \pi}{68}\right) + \frac{5 \pi}{68}$$

=

2*pi
----
 17 

$$\frac{2 \pi}{17}$$

произведение

  3*pi 5*pi
1*----*----
   68   68 

$$\frac{5 \pi}{68} \cdot 1 \cdot \frac{3 \pi}{68}$$

=

     2
15*pi 
------
 4624 

$$\frac{15 \pi^{2}}{4624}$$

Численный ответ

x1 = -46.0612922886621

x2 = -87.7335948406914

x3 = -49.7572836458266

x4 = -28.2281339903436

x5 = 86.2551982978256

x6 = 0.230999459822779

x7 = -63.8020508030515

x8 = 44.2132966100799

x9 = 12.0581718027491

x10 = -101.778361997916

x11 = -13.0745694259693

x12 = -7.99258130986815

x13 = -83.7604041317396

x14 = -2.72579362590879

x15 = -50.7736812690468

x16 = -99.9303663193342

x17 = 46.0612922886621

x18 = -41.9957017957812

x19 = 22.0373484670931

x20 = -55.9480691690771

x21 = -19.7273538688653

x22 = 380.548510112046

x23 = 692.767380008514

x24 = -33.7721210260903

x25 = 39.6857071975534

x26 = -13.1669692098984

x27 = -31.924125347508

x28 = 68.2372404316489

x29 = -5.77498649556947

x30 = 65.6500464816338

x31 = 38.2073106546876

x32 = 92.2611842532179

x33 = -77.7544181763474

x34 = -29.7989303171385

x35 = 88.5651928960534

x36 = -65.9272458334211

x37 = 14.5529659688351

x38 = -91.7991853335723

x39 = 26.0105391760449

x40 = 24.2549432813918

x41 = -197.504538148476

x42 = 18.2489573259995

x43 = -75.9988222816943

x44 = 93.7395807960837

x45 = 101.501162646129

x46 = 78.2164170959929

x47 = 75.9988222816943

x48 = 62.2312544762566

x49 = -53.7304743547784

x50 = -21.944948683164

x51 = 69.992836326302

x52 = 26.4725380956905

x53 = 56.0404689530062

x54 = -39.6857071975534

x55 = -89.9511896549901

x56 = 34.2341199457358

x57 = -11.6885726670326

x58 = 96.2343749621697

x59 = 4.20419016877458

x60 = -97.8051712889646

x61 = 32.2937244832245

x62 = 5.77498649556947

x63 = -39.7781069814825

x64 = 48.5560864547481

x65 = 58.2580637673048

x66 = -67.7752415120033

x67 = 52.2520778119126

x68 = -91.521985981785

x69 = 90.0435894389192

x70 = 82.1896078049447

x71 = -73.7812274673956

x72 = 123.954310140903

x73 = 72.2104311406007

x74 = -43.7512976904343

x75 = -96.9735732336026

x76 = -15.7541631599135

x77 = -9.74817720452127

x78 = 28.2281339903436

x79 = 35.989715840389

x80 = 80.0644127745752

x81 = 87.8259946246205

x82 = -26.3801383117614

x83 = -45.5992933690166

x84 = 41.9957017957812

x85 = 20.5589519242273

x86 = 2.07899513840501

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