sint=−0,2 (уравнение)

Найду корень уравнения: sint=−0,2

Вы ввели

sin(t) = -1/5

$$\sin{\left(t \right)} = - \frac{1}{5}$$

Подробное решение

Дано уравнение
$$\sin{\left(t \right)} = - \frac{1}{5}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{5} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{5} \right)} + \pi$$
Или
$$t = 2 \pi n - \operatorname{asin}{\left(\frac{1}{5} \right)}$$
$$t = 2 \pi n + \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$
, где n - любое целое число

Быстрый ответ

t1 = pi + asin(1/5)

$$t_{1} = \operatorname{asin}{\left(\frac{1}{5} \right)} + \pi$$

t2 = -asin(1/5)

$$t_{2} = - \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Сумма и произведение корней

сумма

0 + pi + asin(1/5) - asin(1/5)

$$- \operatorname{asin}{\left(\frac{1}{5} \right)} + \left(0 + \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right)\right)$$

=

pi

$$\pi$$

произведение

1*(pi + asin(1/5))*-asin(1/5)

$$1 \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \left(- \operatorname{asin}{\left(\frac{1}{5} \right)}\right)$$

=

-(pi + asin(1/5))*asin(1/5)

$$- \left(\operatorname{asin}{\left(\frac{1}{5} \right)} + \pi\right) \operatorname{asin}{\left(\frac{1}{5} \right)}$$

Численный ответ

t1 = -56.7500256854066

t2 = 47.3252477246372

t3 = -15.5066053471586

t4 = -65.7720878045953

t5 = 100.329606994083

t6 = -50.466840378227

t7 = 50.0641245366464

t8 = 97.5907301820739

t9 = -28.0729759615178

t10 = 91.3075448748943

t11 = 9.62613588155971

t12 = 53.6084330318168

t13 = 22.1925064959189

t14 = 62.6304951510055

t15 = 24.931383307928

t16 = 15.9093211887393

t17 = -40.639346575877

t18 = -94.4491375284841

t19 = 41.0420624174576

t20 = -63.0332109925862

t21 = -88.1659522213045

t22 = -2.94023473279946

t23 = -72.0552731117749

t24 = -75.5995816069454

t25 = -9.22342003997905

t26 = -46.9225318830566

t27 = 78.7411742605352

t28 = 9845.55001842962

t29 = -90.9048290333137

t30 = -12.7677285351495

t31 = -34.3561612686974

t32 = 34.7588771102781

t33 = -59.4889024974157

t34 = 72.4579889533556

t35 = -78.3384584189545

t36 = -100.732322835664

t37 = 172.988953868229

t38 = 28.4756918030985

t39 = 4024.58154716932

t40 = 3845.10805007312

t41 = -6.48454322796992

t42 = -21.7897906543382

t43 = -0.201357920790331

t44 = 87.7632363797239

t45 = -31.6172844566883

t46 = 81.4800510725443

t47 = 18.6481980007484

t48 = -37.9004697638678

t49 = -81.882766914125

t50 = 6.08182738638926

t51 = 12.3650126935688

t52 = -97.1880143404933

t53 = 94.0464216869035

t54 = 129.006656717972

t55 = 85.0243595677148

t56 = -44.1836550710474

t57 = 225.993313137675

t58 = 3.34295057438012

t59 = -279.400388248701

t60 = -107.015508142843

t61 = 59.8916183389964

t62 = -25.3340991495087

t63 = -53.2057171902362

t64 = -84.6216437261341

t65 = 31.2145686151076

t66 = -19.0509138423291

t67 = 56.3473098438259

t68 = 43.7809392294668

t69 = -69.3163962997658

t70 = 37.4977539222872

t71 = 66.174803646176

t72 = 75.1968657653647

t73 = 68.9136804581851

График