cos(7*x)=1 (уравнение)

Найду корень уравнения: cos(7*x)=1

Вы ввели

cos(7*x) = 1

$$\cos{\left(7 x \right)} = 1$$

Подробное решение

Дано уравнение
$$\cos{\left(7 x \right)} = 1$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$7 x = \pi n + \operatorname{acos}{\left(1 \right)}$$
$$7 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}$$
Или
$$7 x = \pi n$$
$$7 x = \pi n - \pi$$
, где n - любое целое число
Разделим обе части полученного ур-ния на
$$7$$
получим ответ:
$$x_{1} = \frac{\pi n}{7}$$
$$x_{2} = \frac{\pi n}{7} - \frac{\pi}{7}$$

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

     2*pi
x2 = ----
      7  

$$x_{2} = \frac{2 \pi}{7}$$

Сумма и произведение корней

сумма

2*pi
----
 7  

$$\frac{2 \pi}{7}$$

=

2*pi
----
 7  

$$\frac{2 \pi}{7}$$

произведение

  2*pi
0*----
   7  

$$0 \frac{2 \pi}{7}$$

=

0

$$0$$

Численный ответ

x1 = -60.1390593067073

x2 = -61.9342553369098

x3 = 92.4525837848132

x4 = 58.3438633668186

x5 = -96.0429753720793

x6 = 4.48798961994641

x7 = 58.3438635164292

x8 = -94.2477797830461

x9 = -1.79519576289958

x10 = 68.2174405049031

x11 = -47.5726888024686

x12 = 9.87357697404496

x13 = 35.9039161005348

x14 = 14.3615663614236

x15 = -24.2351434227908

x16 = -11.6687727591318

x17 = 86.1693985784628

x18 = -27.825534858207

x19 = -63.7294509871151

x20 = 19.7471536740575

x21 = 74.500625947435

x22 = 59.241461551491

x23 = -71.8078320294938

x24 = -86.1693984451465

x25 = 84.3742026392561

x26 = 96.0429753281016

x27 = 50.2654824464916

x28 = 87.9645943331678

x29 = 30.5183285125701

x30 = -17.9519581185317

x31 = 0.0

x32 = -65.5246467314959

x33 = 22.4399474878133

x34 = 76.2958215578282

x35 = -87.9645943614492

x36 = 97.8381712684303

x37 = 61.9342552204434

x38 = -81.6814090339112

x39 = -43.9822971752731

x40 = -78.0910173309094

x41 = -21.5423496358453

x42 = -16.1567621600947

x43 = -52.0606782450916

x44 = 53.8558741228462

x45 = 71.8078321175781

x46 = 89.7597899736893

x47 = 70.0126362630036

x48 = 60.1390593781552

x49 = 26.0303390806153

x50 = 42.1871014065155

x51 = -97.838171122323

x52 = -73.6030279418599

x53 = -34.1087201772967

x54 = 17.9519580612321

x55 = -77.1934195630014

x56 = 66.4222446249679

x57 = -55.6510699153731

x58 = -3.59039165971968

x59 = -42.1871013073668

x60 = 32.3135243986474

x61 = 48.4702866788352

x62 = 40.3919054880961

x63 = 52.0606781111898

x64 = 1.79519581891557

x65 = 43.9822971687659

x66 = -83.476604887782

x67 = -45.7774929299455

x68 = -52.060678212119

x69 = 24.2351433392743

x70 = 27.8255349823119

x71 = 94.2477796093549

x72 = 16.1567623135814

x73 = -68.217440491932

x74 = 45.7774929206636

x75 = -8.07838105465554

x76 = 79.8862132535107

x77 = -70.0126362662758

x78 = -29.6207307915393

x79 = -89.7597900950594

x80 = -37.6991118751223

x81 = -26.0303391007703

x82 = -99.6333670698378

x83 = -53.8558739718337

x84 = -91.5549859366252

x85 = 6.28318528501711

x86 = -19.7471538246593

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