cos(x/pi)=1 (уравнение)

Найду корень уравнения: cos(x/pi)=1

Вы ввели

   /x \    
cos|--| = 1
   \pi/    

$$\cos{\left(\frac{x}{\pi} \right)} = 1$$

Подробное решение

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

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

         2
x2 = 2*pi 

$$x_{2} = 2 \pi^{2}$$

Сумма и произведение корней

сумма

            2
0 + 0 + 2*pi 

$$\left(0 + 0\right) + 2 \pi^{2}$$

=

    2
2*pi 

$$2 \pi^{2}$$

произведение

        2
1*0*2*pi 

$$1 \cdot 0 \cdot 2 \pi^{2}$$

=

0

$$0$$

Численный ответ

x1 = -78.95683681936

x2 = 98.6960424267844

x3 = 9.35064998612947e-7

x4 = 39.4784187022512

x5 = 98.6960428476939

x6 = 78.9568357440432

x7 = -39.4784186203696

x8 = 78.9568368285019

x9 = 1.43249603675324e-6

x10 = 19.7392073978248

x11 = -59.2176266837342

x12 = -59.2176279995105

x13 = 59.2176247925263

x14 = 78.9568365065144

x15 = -19.7392051601989

x16 = -39.4784168809644

x17 = 19.739210374246

x18 = -59.217625058035

x19 = -78.9568335875085

x20 = -98.696044525362

x21 = 59.2176272108484

x22 = 78.9568348507788

x23 = 59.2176269059064

x24 = -473.741016048974

x25 = 39.4784176857385

x26 = -78.9568347117588

x27 = 59.2176259305189

x28 = -19.7392103216115

x29 = 1.53065146786522e-6

x30 = 39.4784162705023

x31 = -59.2176264579606

x32 = 19.7392089735332

x33 = -19.7392097183124

x34 = -19.7392072794173

x35 = 59.2176258950712

x36 = 19.7392080989692

x37 = -59.2176257947152

x38 = 78.9568355737134

x39 = 0.0

x40 = -39.4784177567701

x41 = 59.2176276226828

x42 = -39.4784161864643

x43 = -98.6960423963262

x44 = -78.9568346777328

x45 = 19.7392098363507

x46 = -78.9568359981322

x47 = -1.51698804993825e-6

x48 = -98.6960430963433

x49 = 78.9568336023286

x50 = -19.7392048563444

x51 = -19.7392088099943

x52 = -98.6960436319641

x53 = 19.7392100992754

x54 = 98.6960446600283

x55 = 98.6960437743042

x56 = 39.4784187324196

x57 = 19.7392098028537

x58 = 59.2176268248985

x59 = 39.4784192062375

x60 = -78.9568339371924

x61 = 39.4784179023069

x62 = 59.217628025021

x63 = 78.9568340377297

x64 = -39.4784191663784

x65 = -78.9568356060634

x66 = -78.9568364084965

x67 = 39.478416000006

x68 = -39.4784188937958

x69 = -59.2176274941097

x70 = -59.2176247957892

x71 = -8.11688961510312e-7

x72 = 19.7392072284177

x73 = -39.4784160247204

x74 = -39.4784185583403

x75 = -19.7392079708806

x76 = 59.2176251507113

x77 = -19.7392102283976

x78 = -98.696042823225

x79 = -3.91672860930588e-6

x80 = 2.40495448831139e-6

x81 = -19.7392111378321

x82 = -59.2176275172964

x83 = 39.4784170131745

x84 = -1.46651834034308e-6

x85 = 78.9568343072803

x86 = -19.7392073232695

x87 = 98.6960429308937

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