Господин Экзамен

Другие калькуляторы


sin(cos(x))=0

sin(cos(x))=0 уравнение

С верным решением ты станешь самым любимым в группе❤️😊

v

Численное решение:

Искать численное решение на промежутке [, ]

Решение

Вы ввели [src]
sin(cos(x)) = 0
$$\sin{\left(\cos{\left(x \right)} \right)} = 0$$
График
Сумма и произведение корней [src]
сумма
pi   3*pi                                         
-- + ---- + 2*pi - I*im(acos(pi)) + I*im(acos(pi))
2     2                                           
$$\left(\frac{\pi}{2}\right) + \left(\frac{3 \pi}{2}\right) + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right) + \left(i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right)$$
=
4*pi
$$4 \pi$$
произведение
pi   3*pi                                         
-- * ---- * 2*pi - I*im(acos(pi)) * I*im(acos(pi))
2     2                                           
$$\left(\frac{\pi}{2}\right) * \left(\frac{3 \pi}{2}\right) * \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right) * \left(i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}\right)$$
=
    2                                     
3*pi *(2*pi*I + im(acos(pi)))*im(acos(pi))
------------------------------------------
                    4                     
$$\frac{3 \pi^{2} \left(\operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)} + 2 i \pi\right) \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}}{4}$$
Быстрый ответ [src]
      pi
x_1 = --
      2 
$$x_{1} = \frac{\pi}{2}$$
      3*pi
x_2 = ----
       2  
$$x_{2} = \frac{3 \pi}{2}$$
x_3 = 2*pi - I*im(acos(pi))
$$x_{3} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}$$
x_4 = I*im(acos(pi))
$$x_{4} = i \operatorname{im}{\left(\operatorname{acos}{\left(\pi \right)}\right)}$$
Численный ответ [src]
x1 = -95.8185759344887
x2 = 92.6769832808989
x3 = -51.8362787842316
x4 = 39.2699081698724
x5 = -45.553093477052
x6 = -89.5353906273091
x7 = 45.553093477052
x8 = -32.9867228626928
x9 = -61.261056745001
x10 = 86.3937979737193
x11 = 4.71238898038469
x12 = 32.9867228626928
x13 = -83.2522053201295
x14 = 76.9690200129499
x15 = -76.9690200129499
x16 = 89.5353906273091
x17 = 1.5707963267949
x18 = 73.8274273593601
x19 = -73.8274273593601
x20 = 58.1194640914112
x21 = -23.5619449019235
x22 = 26.7035375555132
x23 = -92.6769832808989
x24 = 42.4115008234622
x25 = -80.1106126665397
x26 = 20.4203522483337
x27 = 80.1106126665397
x28 = 29.845130209103
x29 = -86.3937979737193
x30 = -158.650429006285
x31 = -1.5707963267949
x32 = 54.9778714378214
x33 = 23.5619449019235
x34 = -17.2787595947439
x35 = 14.1371669411541
x36 = -98.9601685880785
x37 = 10.9955742875643
x38 = -20.4203522483337
x39 = 17.2787595947439
x40 = 61.261056745001
x41 = -36.1283155162826
x42 = 98.9601685880785
x43 = 36.1283155162826
x44 = -14.1371669411541
x45 = 70.6858347057703
x46 = 95.8185759344887
x47 = -10.9955742875643
x48 = -70.6858347057703
x49 = -4.71238898038469
x50 = 51.8362787842316
x51 = 67.5442420521806
x52 = -7.85398163397448
x53 = -48.6946861306418
x54 = -64.4026493985908
x55 = 7.85398163397448
x56 = -26.7035375555132
x57 = -39.2699081698724
x58 = 64.4026493985908
x59 = -67.5442420521806
x60 = -42.4115008234622
x61 = 48.6946861306418
x62 = -54.9778714378214
x63 = -29.845130209103
x64 = -58.1194640914112
x65 = 83.2522053201295
x65 = 83.2522053201295
График
sin(cos(x))=0 уравнение