sin(x/4)=-1 (уравнение)

Найду корень уравнения: sin(x/4)=-1

Вы ввели

   /x\     
sin|-| = -1
   \4/     

$$\sin{\left(\frac{x}{4} \right)} = -1$$

Подробное решение

Дано уравнение
$$\sin{\left(\frac{x}{4} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{x}{4} = 2 \pi n + \operatorname{asin}{\left(-1 \right)}$$
$$\frac{x}{4} = 2 \pi n - \operatorname{asin}{\left(-1 \right)} + \pi$$
Или
$$\frac{x}{4} = 2 \pi n - \frac{\pi}{2}$$
$$\frac{x}{4} = 2 \pi n + \frac{3 \pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{4}$$
получим ответ:
$$x_{1} = 8 \pi n - 2 \pi$$
$$x_{2} = 8 \pi n + 6 \pi$$

Быстрый ответ

x1 = -2*pi

$$x_{1} = - 2 \pi$$

x2 = 6*pi

$$x_{2} = 6 \pi$$

Сумма и произведение корней

сумма

0 - 2*pi + 6*pi

$$\left(- 2 \pi + 0\right) + 6 \pi$$

=

4*pi

$$4 \pi$$

произведение

1*-2*pi*6*pi

$$6 \pi 1 \left(- 2 \pi\right)$$

=

      2
-12*pi 

$$- 12 \pi^{2}$$

Численный ответ

x1 = -56.5486697349673

x2 = 194.778747866881

x3 = -56.5486683481897

x4 = -56.5486659397182

x5 = -81.6814081736063

x6 = 43.9822933229654

x7 = -81.6814099519144

x8 = 69.1150376557563

x9 = 43.9822992053967

x10 = -81.6814107921866

x11 = -31.4159272035468

x12 = 18.8495538718795

x13 = 43.9822981121978

x14 = 18.8495579062631

x15 = -31.4159258314481

x16 = 94.2477796093523

x17 = 94.2477812103843

x18 = -56.5486665869908

x19 = 973.893722725824

x20 = -81.6814110424777

x21 = 94.2477833024704

x22 = 18.8495565083275

x23 = 18.8495578733093

x24 = 43.9823017225195

x25 = 18.8495560484749

x26 = 69.115036352052

x27 = -303056.876921614

x28 = 18.849554805878

x29 = 18.8495541001135

x30 = 69.1150388458458

x31 = 43.982295127461

x32 = -56.5486674533345

x33 = 69.1150371041081

x34 = 43.982296333884

x35 = -81.6814074129787

x36 = -6.28318386073324

x37 = 94.2477804577374

x38 = -31.4159282896486

x39 = -56.548669162593

x40 = -6.28318679720616

x41 = -31.4159250426185

x42 = -81.6814090382959

x43 = 43.9822955731558

x44 = -56.5486677601098

x45 = -31.4159246188525

x46 = -6.28318512434614

x47 = -31.4159279367377

x48 = 43.9822997316776

x49 = 94.247777948922

x50 = 94.2477779522024

x51 = -6.28318445233127

x52 = -6.283187297182

x53 = 69.115039067239

x54 = -81.6814106031544

x55 = -6.28319034567774

x56 = -56.5486697123861

x57 = 43.9822992138825

x58 = -106.814148184415

x59 = -6.28318423635987

x60 = -31.4159267190222

x61 = -56.5486657062984

x62 = -6.28318720579202

x63 = -6.28318355007082

x64 = -6.28318324372269

x65 = -6.28318600831421

x66 = 18.8495556124419

x67 = 43.9822971694763

x68 = 18.849557322782

x69 = 94.2477786786799

x70 = 94.2477775625785

x71 = 1828.40692636358

x72 = 43.9822988331331

x73 = -81.6814106729198

x74 = 69.1150404081396

x75 = 69.1150364969194

x76 = -81.681406965564

x77 = 69.1150396836239

x78 = -81.6814071728454

x79 = 18.8495547485163

x80 = -81.6814048245694

x81 = -31.4159218307795

x82 = -31.4159285922241

x83 = 94.247781642673

x84 = 43.9822987941229

x85 = -106.814149413349

x86 = -31.4159276033716

x87 = 69.1150402796481

x88 = 43.9822953537312

x89 = -56.5486665882714

x90 = -31.4159245414865

x91 = 69.1150379473762

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