cos x =(3/pi) (уравнение)

Найду корень уравнения: cos x =(3/pi)

Вы ввели

         3 
cos(x) = --
         pi

$$\cos{\left(x \right)} = \frac{3}{\pi}$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = \frac{3}{\pi}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{\pi} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{\pi} \right)}$$
Или
$$x = \pi n + \operatorname{acos}{\left(\frac{3}{\pi} \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{\pi} \right)}$$
, где n - любое целое число

Быстрый ответ

           /3 \       
x1 = - acos|--| + 2*pi
           \pi/       

$$x_{1} = - \operatorname{acos}{\left(\frac{3}{\pi} \right)} + 2 \pi$$

         /3 \
x2 = acos|--|
         \pi/

$$x_{2} = \operatorname{acos}{\left(\frac{3}{\pi} \right)}$$

Численный ответ

x1 = 25.4341148384636

x2 = 44.2836707600024

x3 = -56.247294154871

x4 = -49.9641088476914

x5 = -43.6809235405118

x6 = 49.9641088476914

x7 = 19.150929531284

x8 = 56.8500413743616

x9 = -100.229591305128

x10 = -63.1332266815412

x11 = 0.301373609745291

x12 = 24.8313676189731

x13 = 62.5304794620506

x14 = -37.3977382333322

x15 = -25.4341148384636

x16 = -62.5304794620506

x17 = 835.96501946463

x18 = 43.6809235405118

x19 = 18.5481823117935

x20 = -38.0004854528228

x21 = 5.98181169743429

x22 = -100.832338524619

x23 = -0.301373609745291

x24 = 94.5491532174391

x25 = -18.5481823117935

x26 = 93.9464059979485

x27 = 87.6632206907689

x28 = 56.247294154871

x29 = -24.8313676189731

x30 = -31.7173001456432

x31 = 100.832338524619

x32 = -81.3800353835893

x33 = -301.291521134875

x34 = 100.229591305128

x35 = -94.5491532174391

x36 = 12.2649970046139

x37 = -1960.05244223029

x38 = -75.0968500764098

x39 = -75.6995972959003

x40 = -19.150929531284

x41 = -5.98181169743429

x42 = -12.8677442241045

x43 = -69.4164119887207

x44 = -50.566856067182

x45 = 616.053533713345

x46 = 31.7173001456432

x47 = 12.8677442241045

x48 = -31.1145529261526

x49 = 69.4164119887207

x50 = -88.2659679102595

x51 = 38.0004854528228

x52 = -93.9464059979485

x53 = -12.2649970046139

x54 = -44.2836707600024

x55 = 68.8136647692302

x56 = -56.8500413743616

x57 = 88.2659679102595

x58 = -5856.23007990112

x59 = -68537.2867043247

x60 = 63.1332266815412

x61 = 75.0968500764098

x62 = 6.58455891692488

x63 = 31.1145529261526

x64 = 50.566856067182

x65 = 81.3800353835893

x66 = -6.58455891692488

x67 = 81.9827826030799

x68 = 37.3977382333322

x69 = 75.6995972959003

x70 = -81.9827826030799

x71 = -87.6632206907689

x72 = -68.8136647692302

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