cos(t)=3/11 (уравнение)

Найду корень уравнения: cos(t)=3/11

Вы ввели

cos(t) = 3/11

$$\cos{\left(t \right)} = \frac{3}{11}$$

Подробное решение

Дано уравнение
$$\cos{\left(t \right)} = \frac{3}{11}$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$t = \pi n + \operatorname{acos}{\left(\frac{3}{11} \right)}$$
$$t = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{11} \right)}$$
Или
$$t = \pi n + \operatorname{acos}{\left(\frac{3}{11} \right)}$$
$$t = \pi n - \pi + \operatorname{acos}{\left(\frac{3}{11} \right)}$$
, где n - любое целое число

Быстрый ответ

t1 = -acos(3/11) + 2*pi

$$t_{1} = - \operatorname{acos}{\left(\frac{3}{11} \right)} + 2 \pi$$

t2 = acos(3/11)

$$t_{2} = \operatorname{acos}{\left(\frac{3}{11} \right)}$$

Сумма и произведение корней

сумма

-acos(3/11) + 2*pi + acos(3/11)

$$\operatorname{acos}{\left(\frac{3}{11} \right)} + \left(- \operatorname{acos}{\left(\frac{3}{11} \right)} + 2 \pi\right)$$

=

2*pi

$$2 \pi$$

произведение

(-acos(3/11) + 2*pi)*acos(3/11)

$$\left(- \operatorname{acos}{\left(\frac{3}{11} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{11} \right)}$$

=

(-acos(3/11) + 2*pi)*acos(3/11)

$$\left(- \operatorname{acos}{\left(\frac{3}{11} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{3}{11} \right)}$$

Численный ответ

t1 = -64.1264227678272

t2 = 55.254098068585

t3 = 32.7104962319292

t4 = 23.838171532687

t5 = -13.8609403103905

t6 = 86.6700246044829

t7 = 70.4096080750068

t8 = 82.9759786893659

t9 = 89.2591639965455

t10 = -74.1036539901237

t11 = -11.2718009183279

t12 = 99.2363952188421

t13 = -76.6927933821863

t14 = -118.085951140381

t15 = -89.2591639965455

t16 = -32.7104962319292

t17 = 1318.17434481168

t18 = 36.4045421470462

t19 = -61.5372833757646

t20 = -30.1213568398666

t21 = 92.9532099116625

t22 = 45.2768668462884

t23 = 1.29456969603131

t24 = 20.1441256175701

t25 = 26.4273109247497

t26 = -36.4045421470462

t27 = -82.9759786893659

t28 = -70.4096080750068

t29 = 74.1036539901237

t30 = -48.9709127614054

t31 = -38.9936815391088

t32 = 30.1213568398666

t33 = -4.98861561114828

t34 = 51.560052153468

t35 = -67.8204686829442

t36 = -20.1441256175701

t37 = 76.6927933821863

t38 = 48.9709127614054

t39 = -55.254098068585

t40 = 67.8204686829442

t41 = -23.838171532687

t42 = 64.1264227678272

t43 = -99.2363952188421

t44 = 11.2718009183279

t45 = -86.6700246044829

t46 = 17.5549862255075

t47 = -26.4273109247497

t48 = -80.3868392973033

t49 = 57.8432374606476

t50 = -95.5423493037251

t51 = -57.8432374606476

t52 = -1.29456969603131

t53 = 38.9936815391088

t54 = -42.6877274542258

t55 = 61.5372833757646

t56 = 95.5423493037251

t57 = 80.3868392973033

t58 = 42.6877274542258

t59 = 13.8609403103905

t60 = 7.57775500321089

t61 = -7.57775500321089

t62 = -92.9532099116625

t63 = -51.560052153468

t64 = -45.2768668462884

t65 = -17.5549862255075

t66 = 4.98861561114828

t67 = 363.130178120385

График