sint=sqrt(3)/2 (уравнение)

Найду корень уравнения: sint=sqrt(3)/2

Вы ввели

           ___
         \/ 3 
sin(t) = -----
           2  

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

Подробное решение

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

Быстрый ответ

     pi
t1 = --
     3 

$$t_{1} = \frac{\pi}{3}$$

     2*pi
t2 = ----
      3  

$$t_{2} = \frac{2 \pi}{3}$$

Сумма и произведение корней

сумма

    pi   2*pi
0 + -- + ----
    3     3  

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

=

pi

$$\pi$$

произведение

  pi 2*pi
1*--*----
  3   3  

$$\frac{2 \pi}{3} \cdot 1 \frac{\pi}{3}$$

=

    2
2*pi 
-----
  9  

$$\frac{2 \pi^{2}}{9}$$

Численный ответ

t1 = -23.0383461263252

t2 = 82.7286065445312

t3 = -55.5014702134197

t4 = 38.7463093942741

t5 = 83.7758040957278

t6 = 33.5103216382911

t7 = 146.607657167524

t8 = 95.2949771588904

t9 = 13.6135681655558

t10 = -42.9350995990605

t11 = -104.71975511966

t12 = -99.4837673636768

t13 = -16.7551608191456

t14 = 26.1799387799149

t15 = -5.23598775598299

t16 = -85.870199198121

t17 = -613.657765001206

t18 = 39.7935069454707

t19 = 195.825942073764

t20 = -30.3687289847013

t21 = 27.2271363311115

t22 = 170.693200845045

t23 = -80.634211442138

t24 = 2.0943951023932

t25 = 77.4926187885482

t26 = -79.5870138909414

t27 = 7.33038285837618

t28 = -48.1710873550435

t29 = -49.2182849062401

t30 = 1188.56922060814

t31 = -92.1533845053006

t32 = 71.2094334813686

t33 = 944.572191179331

t34 = -4.18879020478639

t35 = -98.4365698124802

t36 = -74.3510261349584

t37 = -520.457182944709

t38 = -10.471975511966

t39 = -24.0855436775217

t40 = 90.0589894029074

t41 = -6607.81654805053

t42 = -35.6047167406843

t43 = 96.342174710087

t44 = 63.8790506229925

t45 = 8.37758040957278

t46 = 1.0471975511966

t47 = -86.9173967493176

t48 = 51.3126800086333

t49 = 19.8967534727354

t50 = 209.43951023932

t51 = -36.6519142918809

t52 = -61.7846555205993

t53 = -41.8879020478639

t54 = -54.4542726622231

t55 = -29.3215314335047

t56 = 52.3598775598299

t57 = 70.162235930172

t58 = 101.57816246607

t59 = -112.050137978036

t60 = -73.3038285837618

t61 = 76.4454212373516

t62 = 58.6430628670095

t63 = -67.0206432765823

t64 = -11.5191730631626

t65 = 32.4631240870945

t66 = -17.8023583703422

t67 = 57.5958653158129

t68 = 20.943951023932

t69 = -68.0678408277789

t70 = 240.855436775217

t71 = -93.2005820564972

t72 = 89.0117918517108

t73 = 46.0766922526503

t74 = 45.0294947014537

t75 = 64.9262481741891

t76 = 14.6607657167524

t77 = -60.7374579694027

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