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)

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

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)

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

=

pi

$$\pi$$

произведение

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

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

=

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

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

Численный ответ

t1 = 24.4030135724914

t2 = -63.5615807280228

t3 = 98.1190999175106

t4 = -32.1456541921249

t5 = 49.5357548012097

t6 = 36.9693841868506

t7 = 93.5180519514668

t8 = -107.54387787828

t9 = -46.3941621476199

t10 = -38.4288394993045

t11 = -1755.42056570047

t12 = 5.55345765095262

t13 = -101.2606925711

t14 = -90.376459297877

t15 = 412.27836527649

t16 = -57.2783954208432

t17 = 41.5704321528943

t18 = -44.7120248064841

t19 = 79.2695439959718

t20 = -27.5446062260812

t21 = 66.7031733816126

t22 = -84.0932739906975

t23 = -13.2960982705861

t24 = -76.127951342382

t25 = -69.8447660352024

t26 = -7.01291296340655

t27 = 85.5527293031514

t28 = -40.1109768404403

t29 = 74.6684960299281

t30 = -52.6773474547995

t31 = 47.8536174600739

t32 = 55.8189401083893

t33 = 80.9516813371077

t34 = -88.6943219567412

t35 = 60.419988074433

t36 = 87.2348666442873

t37 = -71.5269033763383

t38 = 54.1368027672534

t39 = 35.2872468457147

t40 = 62.1021254155689

t41 = -1979.9330994178

t42 = -0.729727656226966

t43 = -82.4111366495616

t44 = -33.8277915332608

t45 = -77.8100886835179

t46 = 91.835914610331

t47 = 16.4376909241759

t48 = 3.87132030981676

t49 = 10.1545056169963

t50 = 43.2525694940301

t51 = 72.9863586887922

t52 = 99.8012372586464

t53 = 175.199460944801

t54 = 30.686198879671

t55 = -21.2614209189016

t56 = -65.2437180691587

t57 = 22.7208762313555

t58 = -94.9775072639208

t59 = -58.9605327619791

t60 = -50.9952101136637

t61 = -2.41186499736283

t62 = -96.6596446050566

t63 = -836.393373511112

t64 = -14.978235611722

t65 = -19.5792835777657

t66 = -8.69505030454241

t67 = -302.322622400847

t68 = 1216.52608459548

t69 = 11.8366429581322

t70 = 29.0040615385351

t71 = 18.1198282653118

t72 = -25.8624688849453

t73 = 68.3853107227485

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