sin^2x=0 (уравнение)

Найду корень уравнения: sin^2x=0

Вы ввели

   2       
sin (x) = 0

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

Подробное решение

Дано уравнение
$$\sin^{2}{\left(x \right)} = 0$$
преобразуем
$$\sin^{2}{\left(x \right)} = 0$$
$$\sin^{2}{\left(x \right)} + 0 = 0$$
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

$$x_{2} = \pi$$

Сумма и произведение корней

сумма

0 + 0 + pi

$$\left(0 + 0\right) + \pi$$

=

pi

$$\pi$$

произведение

1*0*pi

$$1 \cdot 0 \pi$$

=

0

$$0$$

Численный ответ

x1 = -18.8495556944209

x2 = 84.8230014093114

x3 = -3.14159311568248

x4 = -21.9911485864515

x5 = -12.5663703661411

x6 = -81.6814090380061

x7 = 43.982297169427

x8 = 53.4070756765307

x9 = 84.8230010166547

x10 = 56.5486676091327

x11 = -56.5486675191652

x12 = 21.9911485851964

x13 = -62.8318528379059

x14 = -59.6902604576401

x15 = 59.6902605976901

x16 = -100.530964672522

x17 = -47.1238900492539

x18 = 25.1327414478072

x19 = 53.4070753627408

x20 = -87.9645943587732

x21 = 97.3893727097471

x22 = -94.2477794529919

x23 = 50.2654824463473

x24 = -72.2566308741333

x25 = 91.1061871583643

x26 = 9.42477821024198

x27 = -6.28318513794069

x28 = -31.4159267959754

x29 = -69.1150386253436

x30 = -28.2743337166085

x31 = 47.123890018392

x32 = -97.3893724403711

x33 = -18.8495561207399

x34 = -84.82300141007

x35 = -106.814150357553

x36 = -15.7079632965264

x37 = 3.14159244884412

x38 = -75.3982238620294

x39 = 31.4159267865366

x40 = -34.5575189426108

x41 = -31.4159267051849

x42 = -78.5398160958028

x43 = -91.106187201329

x44 = -25.132741632083

x45 = 15.7079634406648

x46 = 6.28318528425126

x47 = 25.1327410188866

x48 = 34.5575190304759

x49 = 0.0

x50 = -84.8230018263493

x51 = 62.8318528326557

x52 = 28.2743338652012

x53 = 18.8495554002244

x54 = 69.1150385885879

x55 = 91.1061867314459

x56 = 100.530964766599

x57 = -91.1061872003049

x58 = -12.5663700417108

x59 = -34.5575189701076

x60 = 3.14159287686128

x61 = -25.132741473063

x62 = 78.5398161878405

x63 = 69.1150381602162

x64 = 9.42477859080277

x65 = -40.8407042660168

x66 = 72.256631027719

x67 = -43.9822971745789

x68 = 40.840703919946

x69 = 94.2477796093525

x70 = 75.3982241944528

x71 = 47.123889589354

x72 = -69.1150386737158

x73 = -3.14159289677385

x74 = 18.8495556796107

x75 = -1734.15914475848

x76 = -65.9734457650176

x77 = 65.9734457528975

x78 = -47.123890151099

x79 = 31.4159271479423

x80 = 62.8318524523063

x81 = -40.8407046898283

x82 = -37.6991118771514

x83 = 97.3893725148693

x84 = 37.6991120192083

x85 = 75.3982239388525

x86 = -9.42477812668337

x87 = -50.2654822953391

x88 = 12.5663704518704

x89 = 87.9645943357576

x90 = -53.4070752836338

x91 = -62.8318532583801

x92 = 40.8407042560881

x93 = 81.6814091761104

График