cos(t)=-1/2 (уравнение)

Найду корень уравнения: cos(t)=-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

Быстрый ответ

     2*pi
t1 = ----
      3  

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

     4*pi
t2 = ----
      3  

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

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  

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

Численный ответ

t1 = 29.3215314335047

t2 = 27.2271363311115

t3 = 90.0589894029074

t4 = -23.0383461263252

t5 = -58.6430628670095

t6 = -52.3598775598299

t7 = -35.6047167406843

t8 = 10.471975511966

t9 = 2.0943951023932

t10 = 73.3038285837618

t11 = 8.37758040957278

t12 = 96.342174710087

t13 = 77.4926187885482

t14 = 35.6047167406843

t15 = 58.6430628670095

t16 = -67.0206432765823

t17 = -79.5870138909414

t18 = -64.9262481741891

t19 = 117.286125734019

t20 = 67.0206432765823

t21 = 33.5103216382911

t22 = 83.7758040957278

t23 = 416.784625376246

t24 = -20.943951023932

t25 = 23.0383461263252

t26 = 54.4542726622231

t27 = -8.37758040957278

t28 = 20.943951023932

t29 = 4.18879020478639

t30 = -48.1710873550435

t31 = 85.870199198121

t32 = -14.6607657167524

t33 = -16.7551608191456

t34 = -96.342174710087

t35 = 60.7374579694027

t36 = -41.8879020478639

t37 = 41.8879020478639

t38 = -33.5103216382911

t39 = 630.412925820352

t40 = -71.2094334813686

t41 = 98.4365698124802

t42 = 71.2094334813686

t43 = -92.1533845053006

t44 = -54.4542726622231

t45 = -85.870199198121

t46 = -4.18879020478639

t47 = 92.1533845053006

t48 = -98.4365698124802

t49 = 48.1710873550435

t50 = -46.0766922526503

t51 = -39.7935069454707

t52 = -90.0589894029074

t53 = -29.3215314335047

t54 = 52.3598775598299

t55 = -27.2271363311115

t56 = -1623.15620435473

t57 = 39.7935069454707

t58 = -10.471975511966

t59 = 46.0766922526503

t60 = -77.4926187885482

t61 = 64.9262481741891

t62 = -83.7758040957278

t63 = 14.6607657167524

t64 = 79.5870138909414

t65 = -2.0943951023932

t66 = -60.7374579694027

t67 = 16.7551608191456

t68 = -73.3038285837618

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