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
$$t = \pi n + \frac{\pi}{3}$$
$$t = \pi n - \frac{2 \pi}{3}$$
, где n - любое целое число

Быстрый ответ

     pi
t1 = --
     3 

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

     5*pi
t2 = ----
      3  

$$t_{2} = \frac{5 \pi}{3}$$

Сумма и произведение корней

сумма

    pi   5*pi
0 + -- + ----
    3     3  

$$\left(0 + \frac{\pi}{3}\right) + \frac{5 \pi}{3}$$

=

2*pi

$$2 \pi$$

произведение

  pi 5*pi
1*--*----
  3   3  

$$\frac{5 \pi}{3} \cdot 1 \frac{\pi}{3}$$

=

    2
5*pi 
-----
  9  

$$\frac{5 \pi^{2}}{9}$$

Численный ответ

t1 = -63.8790506229925

t2 = 57.5958653158129

t3 = 63.8790506229925

t4 = 49.2182849062401

t5 = 74.3510261349584

t6 = 51.3126800086333

t7 = -45.0294947014537

t8 = -17.8023583703422

t9 = -5.23598775598299

t10 = -24.0855436775217

t11 = 1651.43053823704

t12 = -95.2949771588904

t13 = -89.0117918517108

t14 = 70.162235930172

t15 = -30.3687289847013

t16 = -359.188760060433

t17 = 32.4631240870945

t18 = -38.7463093942741

t19 = 93.2005820564972

t20 = 5.23598775598299

t21 = 61.7846555205993

t22 = -68.0678408277789

t23 = 45.0294947014537

t24 = 80.634211442138

t25 = 1.0471975511966

t26 = 24.0855436775217

t27 = 19.8967534727354

t28 = -11.5191730631626

t29 = 11.5191730631626

t30 = 86.9173967493176

t31 = -61.7846555205993

t32 = 99.4837673636768

t33 = -51.3126800086333

t34 = 82.7286065445312

t35 = -1.0471975511966

t36 = -76.4454212373516

t37 = -7.33038285837618

t38 = 17.8023583703422

t39 = 89.0117918517108

t40 = -13.6135681655558

t41 = 68.0678408277789

t42 = -99.4837673636768

t43 = -80.634211442138

t44 = -19.8967534727354

t45 = 36.6519142918809

t46 = 7.33038285837618

t47 = 76.4454212373516

t48 = -55.5014702134197

t49 = -36.6519142918809

t50 = -225.147473507269

t51 = -57.5958653158129

t52 = -32.4631240870945

t53 = -82.7286065445312

t54 = -42.9350995990605

t55 = 38.7463093942741

t56 = 30.3687289847013

t57 = 55.5014702134197

t58 = 26.1799387799149

t59 = -93.2005820564972

t60 = -70.162235930172

t61 = -74.3510261349584

t62 = 42.9350995990605

t63 = -86.9173967493176

t64 = 95.2949771588904

t65 = 13.6135681655558

t66 = -49.2182849062401

t67 = -26.1799387799149

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