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
$$\frac{x}{4} = 2 \pi n + \frac{\pi}{2}$$
$$\frac{x}{4} = 2 \pi n + \frac{\pi}{2}$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{4}$$
получим ответ:
$$x_{1} = 8 \pi n + 2 \pi$$
$$x_{2} = 8 \pi n + 2 \pi$$

Быстрый ответ

x1 = 2*pi

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

Сумма и произведение корней

сумма

0 + 2*pi

$$0 + 2 \pi$$

=

2*pi

$$2 \pi$$

произведение

1*2*pi

$$1 \cdot 2 \pi$$

=

2*pi

$$2 \pi$$

Численный ответ

x1 = 81.6814083077495

x2 = -43.9822954843527

x3 = -69.1150395658023

x4 = -43.9822962030721

x5 = 6.28318633396377

x6 = 81.6814107598676

x7 = 6.28318528419532

x8 = -94.2477781312881

x9 = -169.645999456262

x10 = 31.4159276708809

x11 = -69.1150394493353

x12 = 106.814148170631

x13 = -18.84955658201

x14 = -94.2477775446078

x15 = -43.9822989304506

x16 = 6.2831871122145

x17 = -94.2477794429042

x18 = -94.2477846569808

x19 = 81.6814104085653

x20 = 31.4159245944257

x21 = 6.28318367405292

x22 = 31.4159264480266

x23 = -69.1150381656234

x24 = -43.9822971745269

x25 = 6.28318325994446

x26 = 81.6814070835547

x27 = -43.9822991766602

x28 = -43.9823007399638

x29 = 81.6814100784289

x30 = -94.2477803243367

x31 = 31.4159268638117

x32 = -245.04423015749

x33 = 56.5486697640327

x34 = -18.8495538879719

x35 = 6.28318689875113

x36 = 6.28318733864694

x37 = -69.1150364335472

x38 = 31.4159245579253

x39 = 56.5486692698042

x40 = 56.5486657084894

x41 = 483.805262524422

x42 = 31.4159251505512

x43 = -18.8495540282808

x44 = 56.5486660203929

x45 = 81.6814075153057

x46 = -43.9822948927238

x47 = -94.2477778601237

x48 = -94.2477785512083

x49 = 6.28318614208925

x50 = 31.4159277260438

x51 = 56.5486696705998

x52 = 31.4159259681666

x53 = -18.849557944068

x54 = 81.6814070084394

x55 = -43.9822979818091

x56 = -94.2477811096296

x57 = 56.5486663320384

x58 = 81.6814091938861

x59 = 81.6814097165964

x60 = 106.814149062976

x61 = 6.28318436335646

x62 = 6.28318363794842

x63 = -43.9822987385722

x64 = -18.8495551717269

x65 = -134830.873503611

x66 = 31.4159285924082

x67 = 56.5486684845824

x68 = -69.1150384130791

x69 = -69.1150402089065

x70 = 31.4159283693215

x71 = -43.9822954777412

x72 = -69.115038704562

x73 = 81.681404123738

x74 = 6.28318923999728

x75 = 6.2831833260163

x76 = -69.1150404265869

x77 = 56.5486727472099

x78 = -18.8495546300962

x79 = -69.1150369903596

x80 = -18.8495572096888

x81 = -43.9822950971527

x82 = -14570.7067218417

x83 = -18.8495554708361

x84 = -69.1150378080493

x85 = 56.5486669680857

x86 = 81.6814110569238

x87 = 56.5486675987755

x88 = 56.5486667114794

x89 = -18.8495563692972

x90 = -94.2477816026358

x91 = -69.1150363870835

x92 = -18.8495578111161

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