sin(x)^2 = 0 (уравнение)

Найду корень уравнения: sin(x)^2 = 0

Вы ввели

   2       
sin (x) = 0

$$\sin^{2}{\left(x \right)} = 0$$

Подробное решение

Дано уравнение
$$\sin^{2}{\left(x \right)} = 0$$
преобразуем
$$\sin^{2}{\left(x \right)} = 0$$
$$\sin^{2}{\left(x \right)} = 0$$
Сделаем замену
$$w = \sin{\left(x \right)}$$
Это уравнение вида

a*w^2 + b*w + c = 0

Квадратное уравнение можно решить
с помощью дискриминанта.
Корни квадратного уравнения:
$$w_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$w_{2} = \frac{- \sqrt{D} - b}{2 a}$$
где D = b^2 - 4*a*c - это дискриминант.
Т.к.
$$a = 1$$
$$b = 0$$
$$c = 0$$
, то

D = b^2 - 4 * a * c = 

(0)^2 - 4 * (1) * (0) = 0

Т.к. D = 0, то корень всего один.

w = -b/2a = -0/2/(1)

$$w_{1} = 0$$
делаем обратную замену
$$\sin{\left(x \right)} = w$$
Дано уравнение
$$\sin{\left(x \right)} = w$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
Или
$$x = 2 \pi n + \operatorname{asin}{\left(w \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(w \right)} + \pi$$
, где n - любое целое число
подставляем w:
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(w_{1} \right)}$$
$$x_{1} = 2 \pi n + \operatorname{asin}{\left(0 \right)}$$
$$x_{1} = 2 \pi n$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(w_{1} \right)} + \pi$$
$$x_{2} = 2 \pi n - \operatorname{asin}{\left(0 \right)} + \pi$$
$$x_{2} = 2 \pi n + \pi$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = pi

$$x_{2} = \pi$$

Численный ответ

x1 = -40.8407046898283

x2 = 40.840703919946

x3 = -75.3982238620294

x4 = 84.8230014093114

x5 = 40.8407042560881

x6 = 75.3982239388525

x7 = -94.2477794529919

x8 = -37.6991118771514

x9 = 97.3893725148693

x10 = -62.8318532583801

x11 = 6.28318528425126

x12 = -28.2743337166085

x13 = 100.530964766599

x14 = 53.4070753627408

x15 = 9.42477821024198

x16 = -81.6814090380061

x17 = 47.123889589354

x18 = -18.8495556944209

x19 = 50.2654824463473

x20 = -1734.15914475848

x21 = 59.6902605976901

x22 = 12.5663704518704

x23 = -12.5663700417108

x24 = 87.9645943357576

x25 = 0.0

x26 = 97.3893727097471

x27 = -97.3893724403711

x28 = 9.42477859080277

x29 = 72.256631027719

x30 = 25.1327410188866

x31 = -91.1061872003049

x32 = 65.9734457528975

x33 = -87.9645943587732

x34 = -18.8495561207399

x35 = -69.1150386253436

x36 = 43.982297169427

x37 = -100.530964672522

x38 = 31.4159271479423

x39 = -12.5663703661411

x40 = 69.1150385885879

x41 = 69.1150381602162

x42 = 25.1327414478072

x43 = -50.2654822953391

x44 = 31.4159267865366

x45 = 53.4070756765307

x46 = 3.14159244884412

x47 = -34.5575189701076

x48 = -84.8230018263493

x49 = -78.5398160958028

x50 = 81.6814091761104

x51 = -47.123890151099

x52 = 84.8230010166547

x53 = -62.8318528379059

x54 = -53.4070752836338

x55 = -25.132741632083

x56 = -25.132741473063

x57 = -21.9911485864515

x58 = -3.14159311568248

x59 = 91.1061867314459

x60 = -31.4159267051849

x61 = 3.14159287686128

x62 = -9.42477812668337

x63 = -43.9822971745789

x64 = -40.8407042660168

x65 = 21.9911485851964

x66 = 91.1061871583643

x67 = -31.4159267959754

x68 = 47.123890018392

x69 = 56.5486676091327

x70 = 15.7079634406648

x71 = 75.3982241944528

x72 = -91.106187201329

x73 = -84.82300141007

x74 = -47.1238900492539

x75 = 34.5575190304759

x76 = -106.814150357553

x77 = -65.9734457650176

x78 = 28.2743338652012

x79 = 62.8318524523063

x80 = 78.5398161878405

x81 = -59.6902604576401

x82 = 62.8318528326557

x83 = -15.7079632965264

x84 = -69.1150386737158

x85 = 18.8495554002244

x86 = -56.5486675191652

x87 = -34.5575189426108

x88 = 37.6991120192083

x89 = 94.2477796093525

x90 = 18.8495556796107

x91 = -3.14159289677385

x92 = -6.28318513794069

x93 = -72.2566308741333

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