sin(t)=-1/2 (уравнение)

Найду корень уравнения: sin(t)=-1/2

Вы ввели

sin(t) = -1/2

$$\sin{\left(t \right)} = - \frac{1}{2}$$

Подробное решение

Дано уравнение
$$\sin{\left(t \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$t = 2 \pi n + \operatorname{asin}{\left(- \frac{1}{2} \right)}$$
$$t = 2 \pi n - \operatorname{asin}{\left(- \frac{1}{2} \right)} + \pi$$
Или
$$t = 2 \pi n - \frac{\pi}{6}$$
$$t = 2 \pi n + \frac{7 \pi}{6}$$
, где n - любое целое число

Быстрый ответ

     -pi 
t1 = ----
      6  

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

     7*pi
t2 = ----
      6  

$$t_{2} = \frac{7 \pi}{6}$$

Сумма и произведение корней

сумма

    pi   7*pi
0 - -- + ----
    6     6  

$$\left(- \frac{\pi}{6} + 0\right) + \frac{7 \pi}{6}$$

=

pi

$$\pi$$

произведение

  -pi  7*pi
1*----*----
   6    6  

$$\frac{7 \pi}{6} \cdot 1 \left(- \frac{\pi}{6}\right)$$

=

     2
-7*pi 
------
  36  

$$- \frac{7 \pi^{2}}{36}$$

Численный ответ

t1 = 28.7979326579064

t2 = 68.5914396033772

t3 = 30.8923277602996

t4 = 37.1755130674792

t5 = -52.8834763354282

t6 = -19.3731546971371

t7 = 192.160750644576

t8 = 66400.1787274983

t9 = 56.025068989018

t10 = 5.75958653158129

t11 = -195.302343298165

t12 = 91.6297857297023

t13 = 9.94837673636768

t14 = -71.733032256967

t15 = 72.7802298081635

t16 = 66.497044500984

t17 = -6.80678408277789

t18 = -50.789081233035

t19 = 437.20497762458

t20 = 81.1578102177363

t21 = -151.320046147908

t22 = -46.6002910282486

t23 = -21.4675497995303

t24 = -25.6563400043166

t25 = 12.0427718387609

t26 = -27.7507351067098

t27 = -13.0899693899575

t28 = -38.2227106186758

t29 = -57.0722665402146

t30 = -31.9395253114962

t31 = 43.4586983746588

t32 = 79.0634151153431

t33 = 53.9306738866248

t34 = 22.5147473507269

t35 = -96.8657734856853

t36 = -0.523598775598299

t37 = 62.3082542961976

t38 = 47.6474885794452

t39 = 74.8746249105567

t40 = 18.3259571459405

t41 = 87.4409955249159

t42 = -40.317105721069

t43 = -88.4881930761125

t44 = 35.081117965086

t45 = 93.7241808320955

t46 = -63.3554518473942

t47 = -75.9218224617533

t48 = -69.6386371545737

t49 = -78.0162175641465

t50 = -82.2050077689329

t51 = -65.4498469497874

t52 = -44.5058959258554

t53 = -101.054563690472

t54 = 41.3643032722656

t55 = 3.66519142918809

t56 = 60.2138591938044

t57 = -15.1843644923507

t58 = -94.7713783832921

t59 = -90.5825881785057

t60 = 49.7418836818384

t61 = 85.3466004225227

t62 = 100.007366139275

t63 = -8.90117918517108

t64 = -84.2994028713261

t65 = 24.60914245312

t66 = -59.1666616426078

t67 = 16.2315620435473

t68 = 97.9129710368819

t69 = -2.61799387799149

t70 = -34.0339204138894

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