sin(t)^(2)=0 (уравнение)

Найду корень уравнения: sin(t)^(2)=0

Вы ввели

   2       
sin (t) = 0

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

Подробное решение

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

Быстрый ответ

t1 = 0

$$t_{1} = 0$$

t2 = pi

$$t_{2} = \pi$$

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

t1 = -12.5663703661411

t2 = 43.982297169427

t3 = 72.256631027719

t4 = 28.2743338652012

t5 = -28.2743337166085

t6 = 84.8230010166547

t7 = 81.6814091761104

t8 = -91.1061872003049

t9 = 31.4159271479423

t10 = 18.8495556796107

t11 = -3.14159311568248

t12 = -94.2477794529919

t13 = 65.9734457528975

t14 = 97.3893727097471

t15 = -97.3893724403711

t16 = -31.4159267051849

t17 = -9.42477812668337

t18 = -62.8318532583801

t19 = 75.3982241944528

t20 = -65.9734457650176

t21 = 3.14159287686128

t22 = -18.8495556944209

t23 = -43.9822971745789

t24 = -6.28318513794069

t25 = 59.6902605976901

t26 = 87.9645943357576

t27 = -56.5486675191652

t28 = -34.5575189426108

t29 = -47.1238900492539

t30 = 78.5398161878405

t31 = 97.3893725148693

t32 = -75.3982238620294

t33 = 25.1327410188866

t34 = 47.123890018392

t35 = -1734.15914475848

t36 = 3.14159244884412

t37 = 75.3982239388525

t38 = -72.2566308741333

t39 = -106.814150357553

t40 = 12.5663704518704

t41 = 91.1061871583643

t42 = 53.4070756765307

t43 = 25.1327414478072

t44 = -84.82300141007

t45 = -18.8495561207399

t46 = -100.530964672522

t47 = 100.530964766599

t48 = 40.8407042560881

t49 = 40.840703919946

t50 = 56.5486676091327

t51 = 0.0

t52 = -37.6991118771514

t53 = -84.8230018263493

t54 = -69.1150386253436

t55 = 6.28318528425126

t56 = -87.9645943587732

t57 = 9.42477821024198

t58 = 37.6991120192083

t59 = -25.132741473063

t60 = -40.8407046898283

t61 = -21.9911485864515

t62 = -81.6814090380061

t63 = 47.123889589354

t64 = 62.8318528326557

t65 = -40.8407042660168

t66 = -62.8318528379059

t67 = 50.2654824463473

t68 = 69.1150385885879

t69 = -12.5663700417108

t70 = -47.123890151099

t71 = -34.5575189701076

t72 = 21.9911485851964

t73 = -3.14159289677385

t74 = 69.1150381602162

t75 = -50.2654822953391

t76 = 34.5575190304759

t77 = -59.6902604576401

t78 = 31.4159267865366

t79 = -53.4070752836338

t80 = 84.8230014093114

t81 = -15.7079632965264

t82 = -78.5398160958028

t83 = -25.132741632083

t84 = 62.8318524523063

t85 = 18.8495554002244

t86 = 94.2477796093525

t87 = 15.7079634406648

t88 = 91.1061867314459

t89 = -69.1150386737158

t90 = 53.4070753627408

t91 = 9.42477859080277

t92 = -31.4159267959754

t93 = -91.106187201329

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