sin(3*t)=1 (уравнение)

Найду корень уравнения: sin(3*t)=1

Вы ввели

sin(3*t) = 1

$$\sin{\left(3 t \right)} = 1$$

Подробное решение

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

Быстрый ответ

     pi
t1 = --
     6 

$$t_{1} = \frac{\pi}{6}$$

Сумма и произведение корней

сумма

    pi
0 + --
    6 

$$0 + \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

произведение

  pi
1*--
  6 

$$1 \frac{\pi}{6}$$

=

pi
--
6 

$$\frac{\pi}{6}$$

Численный ответ

t1 = 0.523598641616331

t2 = -26.7035377567181

t3 = -37.1755131460154

t4 = -66.4970443416682

t5 = -45.5530935835137

t6 = -56.0250689629876

t7 = 78.0162175420896

t8 = -22.5147471967799

t9 = -12.0427717978327

t10 = 19.3731547552869

t11 = 71.733032403968

t12 = 65.4498470876666

t13 = -66.4970445282258

t14 = -81.1578103224548

t15 = 21.4675499464553

t16 = 88.4881929539175

t17 = 8.90117917814493

t18 = -70.6858348165339

t19 = -87.4409956689738

t20 = 67.5442422190054

t21 = -20.4203520794005

t22 = -85.3466004035061

t23 = 84.2994028383437

t24 = 96.865773409958

t25 = -3.66519119284134

t26 = -35.081117920222

t27 = -79.0634150011636

t28 = 27.7507352485908

t29 = -95.8185758682622

t30 = 86.3937978904858

t31 = 92.6769831186997

t32 = -89.5353907407704

t33 = 48.6946859683928

t34 = 94.7713782337162

t35 = -93.7241808501502

t36 = 61.2610563291673

t37 = 54.977871797926

t38 = 90.5825880287766

t39 = 10.9955746928717

t40 = -49.7418836877459

t41 = -7.85398150192478

t42 = -83.252205476317

t43 = 63.3554518703442

t44 = 80.1106131528868

t45 = -58.1194640021532

t46 = -39.2699083292704

t47 = -37.1755131881972

t48 = -53.9306741017977

t49 = 29.845130315527

t50 = -62.308254139164

t51 = -47.6474886422567

t52 = -60.2138590635982

t53 = -85.3466005833809

t54 = 40.31710567763

t55 = 69.6386373203027

t56 = 31.9395253654771

t57 = 23.5619450702353

t58 = 6.8067839497432

t59 = 73.8274274735132

t60 = -91.6297858015358

t61 = 50.789081090574

t62 = -24.6091423681141

t63 = -1.57079642588424

t64 = -43.458698513903

t65 = 46.6002908748595

t66 = -100.007366130834

t67 = 42.411500732115

t68 = 34.0339203588006

t69 = 2.61799372149593

t70 = 52.8834762893477

t71 = -51.8362786904677

t72 = -64.4026492298162

t73 = -5.75958652427337

t74 = 82.2050078076434

t75 = -68.5914394976747

t76 = 4.71238881902407

t77 = -14.1371668430111

t78 = 38.2227106406479

t79 = -9.94837684428868

t80 = -28.7979326032841

t81 = 17.2787592807644

t82 = 25.6563401677065

t83 = -16.2315619072654

t84 = -41.3643034312689

t85 = 44.5058957975625

t86 = 75.9218225274375

t87 = -3.66519148254904

t88 = 98.9601688300381

t89 = -18.3259569854581

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