log(cos(x)) = 0 (уравнение)

Найду корень уравнения: log(cos(x)) = 0

Вы ввели

log(cos(x)) = 0

$$\log{\left(\cos{\left(x \right)} \right)} = 0$$

Подробное решение

Дано уравнение
$$\log{\left(\cos{\left(x \right)} \right)} = 0$$
преобразуем
$$\log{\left(\cos{\left(x \right)} \right)} = 0$$
$$\log{\left(\cos{\left(x \right)} \right)} = 0$$
Сделаем замену
$$w = \cos{\left(x \right)}$$
Дано уравнение
$$\log{\left(w \right)} = 0$$
$$\log{\left(w \right)} = 0$$
Это уравнение вида:

log(v)=p

По определению log

v=e^p

тогда
$$w = e^{\frac{0}{1}}$$
упрощаем
$$w = 1$$
делаем обратную замену
$$\cos{\left(x \right)} = w$$
Дано уравнение
$$\cos{\left(x \right)} = w$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
Или
$$x = \pi n + \operatorname{acos}{\left(w \right)}$$
$$x = \pi n + \operatorname{acos}{\left(w \right)} - \pi$$
, где n - любое целое число
подставляем w:

Быстрый ответ

x1 = 0

$$x_{1} = 0$$

x2 = 2*pi

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

Численный ответ

x1 = 62.831852735923

x2 = 62.8318542034359

x3 = -18.8495565116576

x4 = 18.8495555741382

x5 = 25.1327418930934 + 2.30538452220062e-7*i

x6 = -75.3982238864105

x7 = 69.1150390932802 + 2.7534998623483e-7*i

x8 = -94.2477799001796 - 1.52710927915269e-6*i

x9 = -81.6814090384469

x10 = -50.2654827822791 - 1.52989383343258e-6*i

x11 = -12.5663716386669

x12 = -43.9822971744998

x13 = -31.4159267264704

x14 = 69.1150390127643

x15 = -37.6991118773736

x16 = -75.3982234018825 + 1.49932576193705e-6*i

x17 = -87.9645943584596

x18 = 31.4159269101267

x19 = 37.6991114441887 - 1.53038813166806e-6*i

x20 = 69.1150381807919 - 8.33168149555822e-9*i

x21 = -31.4159262776781 + 1.4972404435276e-6*i

x22 = 94.2477796093522

x23 = -12.5663716213936 - 8.82698796118945e-7*i

x24 = 94.2477796068599 + 1.50254359709193e-6*i

x25 = 56.5486675932357

x26 = -87.9645943355219 - 1.50415742117943e-6*i

x27 = 31.4159255531763

x28 = -37.6991118203008 + 1.48586967313803e-6*i

x29 = -100.53096457631

x30 = 75.3982227418079

x31 = 81.681409203672

x32 = -18.8495553258088

x33 = 37.6991120433529

x34 = -94.2477794374461

x35 = 43.9822971695019

x36 = -6.28318566745615 - 1.53118031064833e-6*i

x37 = -62.8318534517187 - 5.25338389793513e-8*i

x38 = -62.8318528736237 + 9.57612993828518e-7*i

x39 = -50.2654822771894

x40 = 6.28318532165763 + 1.49038506430022e-6*i

x41 = 18.8495570029843

x42 = 75.39822407273

x43 = -56.5486688343165

x44 = -56.5486687640637 - 9.64116384461629e-7*i

x45 = 12.5663704334084

x46 = 62.8318538684035 + 1.2937448235879e-6*i

x47 = 12.5663708485373 + 1.49464065685385e-6*i

x48 = 87.9645943360512

x49 = -100.530965897751 - 1.04338679477469e-6*i

x50 = -25.1327415878584

x51 = 87.9645942296464 - 1.49200746632184e-6*i

x52 = 25.1327406563971

x53 = 25.1327409700176 - 1.9449320805713e-8*i

x54 = -6.28318511692891

x55 = -69.1150373853363

x56 = -18.8495557286473 + 1.05371903118421e-6*i

x57 = -62.8318536803612

x58 = -56.5486674143785

x59 = -25.1327401930409

x60 = 18.8495567580196 + 1.24438528905656e-6*i

x61 = 50.2654824640562 + 1.4959061957848e-6*i

x62 = 69.1150378238503

x63 = 6.28318528416623

x64 = 50.2654824463311

x65 = 56.5486679766099 + 1.49176191840587e-6*i

x66 = -62.8318524940769

x67 = -25.1327403562086 + 1.18933037798285e-6*i

x68 = 81.6814085526449 - 1.52685694226912e-6*i

x69 = 0.0

x70 = 100.530965106382 + 1.48879768924178e-6*i

x71 = -69.1150374752626 + 1.12904165047491e-6*i

x72 = -81.6814089617871 + 1.4822662524172e-6*i

x73 = 25.1327418431203

x74 = 75.3982226911418 - 7.1933410306097e-7*i

x75 = -5.15580584572043e-8 - 1.49585548192749e-6*i

x76 = -12.5663702522378

x77 = 100.530964753022

x78 = 43.982297089421 - 1.49341832886071e-6*i

x79 = -43.9822971932261 - 1.49940218392408e-6*i

x80 = 31.4159255304025 - 8.00625289979724e-7*i

x81 = -18.8495562408585 - 3.41179674495581e-8*i

x82 = -69.1150387500801

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