cost=-1/2 (уравнение)

Найду корень уравнения: cost=-1/2

Вы ввели

cos(t) = -1/2

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

Подробное решение

Дано уравнение
$$\cos{\left(t \right)} = - \frac{1}{2}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$t = \pi n + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
$$t = \pi n - \pi + \operatorname{acos}{\left(- \frac{1}{2} \right)}$$
Или
$$t = \pi n + \frac{2 \pi}{3}$$
$$t = \pi n - \frac{\pi}{3}$$
, где n - любое целое число

Сумма и произведение корней

сумма

    2*pi   4*pi
0 + ---- + ----
     3      3  

$$\left(0 + \frac{2 \pi}{3}\right) + \frac{4 \pi}{3}$$

=

2*pi

$$2 \pi$$

произведение

  2*pi 4*pi
1*----*----
   3    3  

$$\frac{4 \pi}{3} \cdot 1 \cdot \frac{2 \pi}{3}$$

=

    2
8*pi 
-----
  9  

$$\frac{8 \pi^{2}}{9}$$

Быстрый ответ

     2*pi
t1 = ----
      3  

$$t_{1} = \frac{2 \pi}{3}$$

     4*pi
t2 = ----
      3  

$$t_{2} = \frac{4 \pi}{3}$$

Численный ответ

t1 = -20.943951023932

t2 = 39.7935069454707

t3 = 8.37758040957278

t4 = 64.9262481741891

t5 = 83.7758040957278

t6 = -29.3215314335047

t7 = -73.3038285837618

t8 = -46.0766922526503

t9 = -33.5103216382911

t10 = -54.4542726622231

t11 = 67.0206432765823

t12 = -1623.15620435473

t13 = 60.7374579694027

t14 = -79.5870138909414

t15 = -41.8879020478639

t16 = 52.3598775598299

t17 = -16.7551608191456

t18 = 416.784625376246

t19 = -83.7758040957278

t20 = 23.0383461263252

t21 = -27.2271363311115

t22 = 35.6047167406843

t23 = -67.0206432765823

t24 = -23.0383461263252

t25 = 630.412925820352

t26 = 20.943951023932

t27 = -96.342174710087

t28 = 73.3038285837618

t29 = -52.3598775598299

t30 = 16.7551608191456

t31 = -14.6607657167524

t32 = 14.6607657167524

t33 = 96.342174710087

t34 = 29.3215314335047

t35 = 54.4542726622231

t36 = 117.286125734019

t37 = 41.8879020478639

t38 = 98.4365698124802

t39 = 27.2271363311115

t40 = 77.4926187885482

t41 = -92.1533845053006

t42 = -2.0943951023932

t43 = 10.471975511966

t44 = -4.18879020478639

t45 = 92.1533845053006

t46 = -35.6047167406843

t47 = -10.471975511966

t48 = -39.7935069454707

t49 = -77.4926187885482

t50 = -8.37758040957278

t51 = 79.5870138909414

t52 = 85.870199198121

t53 = 58.6430628670095

t54 = -71.2094334813686

t55 = -90.0589894029074

t56 = -58.6430628670095

t57 = 4.18879020478639

t58 = 48.1710873550435

t59 = 90.0589894029074

t60 = 2.0943951023932

t61 = -60.7374579694027

t62 = 33.5103216382911

t63 = 46.0766922526503

t64 = -64.9262481741891

t65 = 71.2094334813686

t66 = -85.870199198121

t67 = -98.4365698124802

t68 = -48.1710873550435

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