cos(t/5)=-1 (уравнение)

Найду корень уравнения: cos(t/5)=-1

Вы ввели

   /t\     
cos|-| = -1
   \5/     

$$\cos{\left(\frac{t}{5} \right)} = -1$$

Подробное решение

Дано уравнение
$$\cos{\left(\frac{t}{5} \right)} = -1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$\frac{t}{5} = \pi n + \operatorname{acos}{\left(-1 \right)}$$
$$\frac{t}{5} = \pi n - \pi + \operatorname{acos}{\left(-1 \right)}$$
Или
$$\frac{t}{5} = \pi n + \pi$$
$$\frac{t}{5} = \pi n$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$\frac{1}{5}$$
получим ответ:
$$t_{1} = 5 \pi n + 5 \pi$$
$$t_{2} = 5 \pi n$$

Быстрый ответ

t1 = 5*pi

$$t_{1} = 5 \pi$$

Сумма и произведение корней

сумма

0 + 5*pi

$$0 + 5 \pi$$

=

5*pi

$$5 \pi$$

произведение

1*5*pi

$$1 \cdot 5 \pi$$

=

5*pi

$$5 \pi$$

Численный ответ

t1 = 47.123891073275

t2 = -47.1238889196755

t3 = 204.203522241035

t4 = -15.7079609905632

t5 = -78.5398187594684

t6 = -78.5398151446878

t7 = 15.707961729282

t8 = 47.1238873084304

t9 = 109.955740633841

t10 = 78.5398137772168

t11 = 78.5398189021442

t12 = 47.1238923027174

t13 = -47.1238901257198

t14 = -47.1238876815792

t15 = 47.1238877741124

t16 = -47.1238913784282

t17 = 15.7079601534269

t18 = 47.123892306231

t19 = -78.5398184687978

t20 = 78.5398170682907

t21 = 15.7079630812848

t22 = 47.1238911368643

t23 = 78.539819441708

t24 = -47.1238922564323

t25 = -15.707963787485

t26 = -15.707965329034

t27 = -47.123891755735

t28 = 78.5398186830988

t29 = 47.1238961171027

t30 = -47.1238892266369

t31 = -78.5398146753102

t32 = 15.7079610707134

t33 = 15.7079600690302

t34 = 47.1238834902891

t35 = -15.7079656074579

t36 = -15.7079614567185

t37 = -15.7079606929945

t38 = -78.5398170658543

t39 = -78.5398177822968

t40 = -78.5398169297615

t41 = 15.7079651530831

t42 = -78.5398138890222

t43 = -78.5398160322833

t44 = 78.5398144993885

t45 = -47.1238872711186

t46 = -47.1238923366349

t47 = 15.7079651296196

t48 = -15.7079642265323

t49 = -109.955744308027

t50 = -15.707965838961

t51 = 47.1238893672005

t52 = -47.1238873586036

t53 = 15.7079647632944

t54 = 78.5398220572023

t55 = -15.7079616129238

t56 = -15.7079624295751

t57 = -15.7079610256452

t58 = 78.5398165209218

t59 = 47.123888495739

t60 = 78.539818554401

t61 = 15.7079656734751

t62 = 78.5398144533592

t63 = 15.7079609259173

t64 = 78.5398139484401

t65 = 78.5398152747855

t66 = 15.707962566483

t67 = -15.7079632966218

t68 = 47.1238918530452

t69 = 47.1238885314361

t70 = -78.5398188712212

t71 = 47.1238873132795

t72 = 47.1238902678764

t73 = -47.1238845327779

t74 = -109.955740761569

t75 = 78.5398179019981

t76 = 109.955743388045

t77 = -109.955745597958

t78 = -78.5398143960206

t79 = 1523.672431799

t80 = -78.5398137921376

t81 = -141.371669109372

t82 = 15.7079634553212

t83 = -78.5398210333058

t84 = -47.1238910102026

t85 = 15.7079607148849

t86 = -15.7079650220913

t87 = 15.7079643589024

t88 = 78.5398161781999

t89 = 15.7079658362819

t90 = -47.1238883718742

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