cos(t)=2/3 (уравнение)

Найду корень уравнения: cos(t)=2/3

Вы ввели

cos(t) = 2/3

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

Подробное решение

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

Быстрый ответ

t1 = -acos(2/3) + 2*pi

$$t_{1} = - \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi$$

t2 = acos(2/3)

$$t_{2} = \operatorname{acos}{\left(\frac{2}{3} \right)}$$

Сумма и произведение корней

сумма

0 + -acos(2/3) + 2*pi + acos(2/3)

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

=

2*pi

$$2 \pi$$

произведение

1*(-acos(2/3) + 2*pi)*acos(2/3)

$$1 \left(- \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{3} \right)}$$

=

(-acos(2/3) + 2*pi)*acos(2/3)

$$\left(- \operatorname{acos}{\left(\frac{2}{3} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{2}{3} \right)}$$

Численный ответ

t1 = 43.1412284796892

t2 = -76.239292356723

t3 = 19.6906245921067

t4 = -13.4074392849271

t5 = 11.7253019437912

t6 = 49.4244137868688

t7 = 57.3897364351842

t8 = 18.0084872509708

t9 = -49.4244137868688

t10 = -32.2569952064659

t11 = -44.823365820825

t12 = -5.44211663661166

t13 = 93.4067109371259

t14 = 38.5401805136454

t15 = -68.2739697084075

t16 = -7.12425397774752

t17 = 88.8056629710821

t18 = -63.6729217423638

t19 = -43.1412284796892

t20 = 68.2739697084075

t21 = 44.823365820825

t22 = -36.8580431725096

t23 = -99.6898962443055

t24 = 99.6898962443055

t25 = 82.5224776639025

t26 = 25.9738098992863

t27 = -30.57485786533

t28 = 55.7075990940483

t29 = 80.8403403227667

t30 = 95.0888482782617

t31 = 61.9907844012279

t32 = -51.1065511280046

t33 = 69.9561070495434

t34 = 87.1235256299463

t35 = -55.7075990940483

t36 = -101.372033585441

t37 = -38.5401805136454

t38 = 7.12425397774752

t39 = -18.0084872509708

t40 = 63.6729217423638

t41 = -69.9561070495434

t42 = -95.0888482782617

t43 = -87.1235256299463

t44 = -93.4067109371259

t45 = 36.8580431725096

t46 = 51.1065511280046

t47 = -57.3897364351842

t48 = -82.5224776639025

t49 = -74.5571550155871

t50 = -19.6906245921067

t51 = -88.8056629710821

t52 = -80.8403403227667

t53 = 5.44211663661166

t54 = -0.84106867056793

t55 = 0.84106867056793

t56 = -11.7253019437912

t57 = 13.4074392849271

t58 = 32.2569952064659

t59 = 76.239292356723

t60 = 74.5571550155871

t61 = -25.9738098992863

t62 = -61.9907844012279

t63 = 30.57485786533

t64 = -24.2916725581504

t65 = 24.2916725581504

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