Дано
$$frac{e^{- 1000000 t}}{frac{24649 f^{2}}{625} + 1000000000000} left(frac{157 f}{25} sin{left (frac{157 f}{25} t right )} – 1000000 cos{left (frac{157 f}{25} t right )}right)$$
Подстановка условия
$$frac{e^{- 1000000 t}}{frac{24649 f^{2}}{625} + 1000000000000} left(frac{157 f}{25} sin{left (frac{157 f}{25} t right )} – 1000000 cos{left (frac{157 f}{25} t right )}right)$$
((-3)^(-1000000*t)*(((157*f)*sin(((157*f)*t)/25))/25 – 1000000*cos(((157*f)*t)/25)))/(1000000000000 + (24649*f^2)/625)
$$frac{(-3)^{- 1000000 t}}{frac{24649 f^{2}}{625} + 1000000000000} left(frac{157 f}{25} sin{left (frac{157 f}{25} t right )} – 1000000 cos{left (frac{157 f}{25} t right )}right)$$
((-3)^(-1000000*t)*(((157*f)*sin(((157*f)*t)/25))/25 – 1000000*cos(((157*f)*t)/25)))/(1000000000000 + (24649*f^2)/625)
$$frac{left(-3right)^{- 1000000 t}}{frac{24649 f^{2}}{625} + 1000000000000} left(frac{157 f}{25} sin{left (frac{157 f}{25} t right )} – 1000000 cos{left (frac{157 f}{25} t right )}right)$$
(-3)^(-1000000*t)*(-1000000*cos(157*f*t/25) + 157*f*sin(157*f*t/25)/25)/(1000000000000 + 24649*f^2/625)
$$frac{left(-3right)^{- 1000000 t}}{frac{24649 f^{2}}{625} + 1000000000000} left(frac{157 f}{25} sin{left (frac{157 f}{25} t right )} – 1000000 cos{left (frac{157 f}{25} t right )}right)$$
Численный ответ
2.71828182845905^(-1000000.0*t)*(-1000000.0*cos(((157*f)*t)/25) + 6.28*f*sin(((157*f)*t)/25))/(1000000000000.0 + 39.4384*f^2)
Рациональный знаменатель
$$frac{e^{- 1000000 t}}{616225 f^{2} + 15625000000000000} left(98125 f sin{left (frac{157 f}{25} t right )} – 15625000000 cos{left (frac{157 f}{25} t right )}right)$$
Объединение рациональных выражений
$$frac{25 e^{- 1000000 t}}{24649 f^{2} + 625000000000000} left(157 f sin{left (frac{157 f}{25} t right )} – 25000000 cos{left (frac{157 f}{25} t right )}right)$$
Общее упрощение
/ /157*f*t /157*f*t -1000000*t
|- 625000000*cos|——-| + 3925*f*sin|——-||*e
25 / 25 //
————————————————————
2
625000000000000 + 24649*f
$$frac{e^{- 1000000 t}}{24649 f^{2} + 625000000000000} left(3925 f sin{left (frac{157 f}{25} t right )} – 625000000 cos{left (frac{157 f}{25} t right )}right)$$
Соберем выражение
$$frac{3925 f sin{left (frac{157 f}{25} t right )}}{24649 f^{2} e^{1000000 t} + 625000000000000 e^{1000000 t}} – frac{625000000 cos{left (frac{157 f}{25} t right )}}{24649 f^{2} e^{1000000 t} + 625000000000000 e^{1000000 t}}$$
Общий знаменатель
/157*f*t /157*f*t
– 625000000*cos|——-| + 3925*f*sin|——-|
25 / 25 /
————————————————
1000000*t 2 1000000*t
625000000000000*e + 24649*f *e
$$frac{3925 f sin{left (frac{157 f}{25} t right )} – 625000000 cos{left (frac{157 f}{25} t right )}}{24649 f^{2} e^{1000000 t} + 625000000000000 e^{1000000 t}}$$
Комбинаторика
/ /157*f*t /157*f*t -1000000*t
25*|- 25000000*cos|——-| + 157*f*sin|——-||*e
25 / 25 //
————————————————————-
2
625000000000000 + 24649*f
$$frac{25 e^{- 1000000 t}}{24649 f^{2} + 625000000000000} left(157 f sin{left (frac{157 f}{25} t right )} – 25000000 cos{left (frac{157 f}{25} t right )}right)$$
