sin(t)=2/3 (уравнение)

Найду корень уравнения: sin(t)=2/3

Вы ввели

sin(t) = 2/3

$$\sin{\left(t \right)} = \frac{2}{3}$$

Подробное решение

Дано уравнение
$$\sin{\left(t \right)} = \frac{2}{3}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
Или
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{2}{3} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{2}{3} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

t1 = pi - asin(2/3)

$$t_{1} = \pi - \operatorname{asin}{\left(\frac{2}{3} \right)}$$

t2 = asin(2/3)

$$t_{2} = \operatorname{asin}{\left(\frac{2}{3} \right)}$$

Сумма и произведение корней

сумма

0 + pi - asin(2/3) + asin(2/3)

$$\operatorname{asin}{\left(\frac{2}{3} \right)} + \left(0 + \left(\pi - \operatorname{asin}{\left(\frac{2}{3} \right)}\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi - asin(2/3))*asin(2/3)

$$1 \left(\pi - \operatorname{asin}{\left(\frac{2}{3} \right)}\right) \operatorname{asin}{\left(\frac{2}{3} \right)}$$

=

(pi - asin(2/3))*asin(2/3)

$$\left(\pi - \operatorname{asin}{\left(\frac{2}{3} \right)}\right) \operatorname{asin}{\left(\frac{2}{3} \right)}$$

Численный ответ

t1 = -91.835914610331

t2 = -123.251841146229

t3 = 915594.458012514

t4 = 21.2614209189016

t5 = -104.40228522469

t6 = -47.8536174600739

t7 = -68.3853107227485

t8 = -87.2348666442873

t9 = -189567.572037918

t10 = 84.0932739906975

t11 = -98.1190999175106

t12 = 69.8447660352024

t13 = -54.1368027672534

t14 = -11.8366429581322

t15 = -55.8189401083893

t16 = -809.80117696994

t17 = -72.9863586887922

t18 = 25.8624688849453

t19 = -161594.831050354

t20 = -85.5527293031514

t21 = -43.2525694940301

t22 = 1485.24359749175

t23 = -3.87132030981676

t24 = 90.376459297877

t25 = 94.9775072639208

t26 = 222.323350748648

t27 = 46.3941621476199

t28 = -30.686198879671

t29 = 101.2606925711

t30 = 96.6596446050566

t31 = 44.7120248064841

t32 = -1241.6588258242

t33 = -16.4376909241759

t34 = 88.6943219567412

t35 = 14.978235611722

t36 = 50.9952101136637

t37 = 8206.56973883277

t38 = 4876.48152602759

t39 = -93.5180519514668

t40 = -24.4030135724914

t41 = 33.8277915332608

t42 = -66.7031733816126

t43 = -35.2872468457147

t44 = 76.127951342382

t45 = -5.55345765095262

t46 = -74.6684960299281

t47 = 2.41186499736283

t48 = 38.4288394993045

t49 = 52.6773474547995

t50 = -29.0040615385351

t51 = 40.1109768404403

t52 = 8.69505030454241

t53 = 27.5446062260812

t54 = -79.2695439959718

t55 = 63.5615807280228

t56 = 57.2783954208432

t57 = 19.5792835777657

t58 = 13.2960982705861

t59 = -62.1021254155689

t60 = -49.5357548012097

t61 = -10.1545056169963

t62 = 32.1456541921249

t63 = 0.729727656226966

t64 = 71.5269033763383

t65 = 352.588104858284

t66 = 77.8100886835179

t67 = 82.4111366495616

t68 = -80.9516813371077

t69 = -41.5704321528943

t70 = 7.01291296340655

t71 = -99.8012372586464

t72 = -22.7208762313555

t73 = 58.9605327619791

t74 = -36.9693841868506

t75 = 65.2437180691587

t76 = -18.1198282653118

t77 = -60.419988074433

t78 = -2033.34017452882

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