cos(x)=i (уравнение)

Найду корень уравнения: cos(x)=i

Вы ввели

cos(x) = I

$$\cos{\left(x \right)} = i$$

Подробное решение

Дано уравнение
$$\cos{\left(x \right)} = i$$
- это простейшее тригонометрическое ур-ние
Это ур-ние преобразуется в
$$x = \pi n + \operatorname{acos}{\left(i \right)}$$
$$x = \pi n - \pi + \operatorname{acos}{\left(i \right)}$$
Или
$$x = \pi n + \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
$$x = \pi n - \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
, где n - любое целое число

Быстрый ответ

     pi        /      ___\
x1 = -- - I*log\1 + \/ 2 /
     2                    

$$x_{1} = \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$

     3*pi        /      ___\
x2 = ---- + I*log\1 + \/ 2 /
      2                     

$$x_{2} = \frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}$$

Численный ответ

x1 = -61.261056745001 - 0.881373587019543*i

x2 = 45.553093477052 - 0.881373587019543*i

x3 = -64.4026493985908 + 0.881373587019543*i

x4 = 1.5707963267949 - 0.881373587019543*i

x5 = -1.5707963267949 + 0.881373587019543*i

x6 = 51.8362787842316 - 0.881373587019543*i

x7 = -89.5353906273091 + 0.881373587019543*i

x8 = -45.553093477052 + 0.881373587019543*i

x9 = 10.9955742875643 + 0.881373587019543*i

x10 = 98.9601685880785 + 0.881373587019543*i

x11 = 26.7035375555132 - 0.881373587019543*i

x12 = 42.4115008234622 + 0.881373587019543*i

x13 = -48.6946861306418 - 0.881373587019543*i

x14 = -86.3937979737193 - 0.881373587019543*i

x15 = 29.845130209103 + 0.881373587019543*i

x16 = -92.6769832808989 - 0.881373587019543*i

x17 = -39.2699081698724 + 0.881373587019543*i

x18 = 61.261056745001 + 0.881373587019543*i

x19 = 70.6858347057703 - 0.881373587019543*i

x20 = -51.8362787842316 + 0.881373587019543*i

x21 = -67.5442420521806 - 0.881373587019543*i

x22 = 20.4203522483337 - 0.881373587019543*i

x23 = -73.8274273593601 - 0.881373587019543*i

x24 = -95.8185759344887 + 0.881373587019543*i

x25 = 73.8274273593601 + 0.881373587019543*i

x26 = -54.9778714378214 - 0.881373587019543*i

x27 = -17.2787595947439 - 0.881373587019543*i

x28 = 48.6946861306418 + 0.881373587019543*i

x29 = -29.845130209103 - 0.881373587019543*i

x30 = -58.1194640914112 + 0.881373587019543*i

x31 = 58.1194640914112 - 0.881373587019543*i

x32 = 32.9867228626928 - 0.881373587019543*i

x33 = -83.2522053201295 + 0.881373587019543*i

x34 = 89.5353906273091 - 0.881373587019543*i

x35 = 86.3937979737193 + 0.881373587019543*i

x36 = 36.1283155162826 + 0.881373587019543*i

x37 = 83.2522053201295 - 0.881373587019543*i

x38 = 17.2787595947439 + 0.881373587019543*i

x39 = -32.9867228626928 + 0.881373587019543*i

x40 = 54.9778714378214 + 0.881373587019543*i

x41 = -14.1371669411541 + 0.881373587019543*i

x42 = -80.1106126665397 - 0.881373587019543*i

x43 = -4.71238898038469 - 0.881373587019543*i

x44 = 67.5442420521806 + 0.881373587019543*i

x45 = 92.6769832808989 + 0.881373587019543*i

x46 = 64.4026493985908 - 0.881373587019543*i

x47 = 23.5619449019235 + 0.881373587019543*i

x48 = 76.9690200129499 - 0.881373587019543*i

x49 = -23.5619449019235 - 0.881373587019543*i

x50 = -36.1283155162826 - 0.881373587019543*i

x51 = -10.9955742875643 - 0.881373587019543*i

x52 = 80.1106126665397 + 0.881373587019543*i

x53 = 4.71238898038469 + 0.881373587019543*i

x54 = -7.85398163397448 + 0.881373587019543*i

x55 = 39.2699081698724 - 0.881373587019543*i

x56 = 7.85398163397448 - 0.881373587019543*i

x57 = 95.8185759344887 - 0.881373587019543*i

x58 = -42.4115008234622 - 0.881373587019543*i

x59 = -98.9601685880785 - 0.881373587019543*i

x60 = 14.1371669411541 - 0.881373587019543*i

x61 = -70.6858347057703 + 0.881373587019543*i

x62 = -76.9690200129499 + 0.881373587019543*i

x63 = -20.4203522483337 + 0.881373587019543*i

x64 = -26.7035375555132 + 0.881373587019543*i