Дано
$$frac{1}{100} 103 left(frac{7}{10} sin{left (14 t right )} + frac{4}{5} sin{left (25 t right )} + 2 sin{left (35 t right )}right) cos{left (5966 t right )} + frac{33}{10}$$
Подстановка условия
$$frac{1}{100} 103 left(frac{7}{10} sin{left (14 t right )} + frac{4}{5} sin{left (25 t right )} + 2 sin{left (35 t right )}right) cos{left (5966 t right )} + frac{33}{10}$$
33/10 + ((103*((7*sin(14*(-1/2)))/10 + (4*sin(25*(-1/2)))/5 + 2*sin(35*(-1/2))))*cos(5966*(-1/2)))/100
$$frac{1}{100} 103 left(frac{7}{10} sin{left (14 (-1/2) right )} + frac{4}{5} sin{left (25 (-1/2) right )} + 2 sin{left (35 (-1/2) right )}right) cos{left (5966 (-1/2) right )} + frac{33}{10}$$
33/10 + ((103*((7*sin(14*(-1)/2))/10 + (4*sin(25*(-1)/2))/5 + 2*sin(35*(-1)/2)))*cos(5966*(-1)/2))/100
$$frac{1}{100} 103 left(frac{7}{10} sin{left (frac{-14}{2} right )} + frac{4}{5} sin{left (frac{-25}{2} right )} + 2 sin{left (frac{-35}{2} right )}right) cos{left (frac{-5966}{2} right )} + frac{33}{10}$$
33/10 + (-206*sin(35/2) – 721*sin(7)/10 – 412*sin(25/2)/5)*cos(2983)/100
$$frac{1}{100} left(- frac{721}{10} sin{left (7 right )} – frac{412}{5} sin{left (frac{25}{2} right )} – 206 sin{left (frac{35}{2} right )}right) cos{left (2983 right )} + frac{33}{10}$$
Степени
$$frac{1}{100} left(frac{721}{10} sin{left (14 t right )} + frac{412}{5} sin{left (25 t right )} + 206 sin{left (35 t right )}right) cos{left (5966 t right )} + frac{33}{10}$$
Численный ответ
3.3 + 1.03*(2.0*sin(35*t) + 0.8*sin(25*t) + 0.7*sin(14*t))*cos(5966*t)
Рациональный знаменатель
$$frac{1}{5000} left(3605 sin{left (14 t right )} + 4120 sin{left (25 t right )} + 10300 sin{left (35 t right )}right) cos{left (5966 t right )} + frac{33}{10}$$
Объединение рациональных выражений
$$frac{1}{1000} left(103 left(7 sin{left (14 t right )} + 8 sin{left (25 t right )} + 20 sin{left (35 t right )}right) cos{left (5966 t right )} + 3300right)$$
Общее упрощение
33 103*(7*sin(14*t) + 8*sin(25*t) + 20*sin(35*t))*cos(5966*t)
— + ———————————————————-
10 1000
$$frac{103}{1000} left(7 sin{left (14 t right )} + 8 sin{left (25 t right )} + 20 sin{left (35 t right )}right) cos{left (5966 t right )} + frac{33}{10}$$
Соберем выражение
$$- frac{103}{100} sin{left (5931 t right )} – frac{103}{250} sin{left (5941 t right )} – frac{721}{2000} sin{left (5952 t right )} + frac{721}{2000} sin{left (5980 t right )} + frac{103}{250} sin{left (5991 t right )} + frac{103}{100} sin{left (6001 t right )} + frac{33}{10}$$
Общий знаменатель
33 103*cos(5966*t)*sin(35*t) 103*cos(5966*t)*sin(25*t) 721*cos(5966*t)*sin(14*t)
— + ————————- + ————————- + ————————-
10 50 125 1000
$$frac{721}{1000} sin{left (14 t right )} cos{left (5966 t right )} + frac{103}{125} sin{left (25 t right )} cos{left (5966 t right )} + frac{103}{50} sin{left (35 t right )} cos{left (5966 t right )} + frac{33}{10}$$
Тригонометрическая часть
/ 103*(7*sin(14*t) + 8*sin(25*t))
|206*sin(35*t) + ——————————-|*cos(5966*t)
33 10 /
— + ————————————————————-
10 100
$$frac{1}{100} left(frac{1}{10} left(721 sin{left (14 t right )} + 824 sin{left (25 t right )}right) + 206 sin{left (35 t right )}right) cos{left (5966 t right )} + frac{33}{10}$$
Комбинаторика
3300 + 721*cos(5966*t)*sin(14*t) + 824*cos(5966*t)*sin(25*t) + 2060*cos(5966*t)*sin(35*t)
—————————————————————————————–
1000
$$frac{1}{1000} left(721 sin{left (14 t right )} cos{left (5966 t right )} + 824 sin{left (25 t right )} cos{left (5966 t right )} + 2060 sin{left (35 t right )} cos{left (5966 t right )} + 3300right)$$
