Дано
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} x right )} – 2 frac{1}{17 pi} sin{left (frac{17 pi}{4} x right )}$$
Подстановка условия
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} x right )} – 2 frac{1}{17 pi} sin{left (frac{17 pi}{4} x right )}$$
(2*sin(((15*pi)*(-1/3))/4))/(15*pi) – 2*sin(((17*pi)*(-1/3))/4)/17*pi
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} (-1/3) right )} – 2 frac{1}{17 pi} sin{left (frac{17 pi}{4} (-1/3) right )}$$
(2*sin(((15*pi)*(-1)/3)/4))/(15*pi) – 2*sin(((17*pi)*(-1)/3)/4)/17*pi
$$- 2 frac{1}{17 pi} sin{left (frac{17 pi}{4} – frac{1}{3} right )} + frac{2}{15 pi} sin{left (frac{15 pi}{4} – frac{1}{3} right )}$$
-(sqrt(2)/2 + sqrt(6)/2)/(17*pi) + sqrt(2)/(15*pi)
$$- frac{frac{sqrt{2}}{2} + frac{sqrt{6}}{2}}{17 pi} + frac{sqrt{2}}{15 pi}$$
Степени
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} x right )} – frac{2}{17 pi} sin{left (frac{17 pi}{4} x right )}$$
Численный ответ
0.0424413181578388*sin(((15*pi)*x)/4) – 0.0374482219039754*sin(((17*pi)*x)/4)
Рациональный знаменатель
$$frac{1}{255 pi^{2}} left(34 pi sin{left (frac{15 pi}{4} x right )} – 30 pi sin{left (frac{17 pi}{4} x right )}right)$$
Объединение рациональных выражений
$$frac{1}{255 pi} left(34 sin{left (frac{15 pi}{4} x right )} – 30 sin{left (frac{17 pi}{4} x right )}right)$$
Общее упрощение
/ /17*pi*x /15*pi*x
2*|- 15*sin|——-| + 17*sin|——-||
4 / 4 //
—————————————
255*pi
$$frac{1}{255 pi} left(34 sin{left (frac{15 pi}{4} x right )} – 30 sin{left (frac{17 pi}{4} x right )}right)$$
Соберем выражение
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} x right )} – frac{2 pi}{17} sin{left (frac{17 pi}{4} x right )}$$
Общий знаменатель
/17*pi*x /15*pi*x
– 30*sin|——-| + 34*sin|——-|
4 / 4 /
———————————–
255*pi
$$frac{1}{255 pi} left(34 sin{left (frac{15 pi}{4} x right )} – 30 sin{left (frac{17 pi}{4} x right )}right)$$
Тригонометрическая часть
/ /17*pi*x /15*pi*x
2*|- 15*sin|——-| + 17*sin|——-||
4 / 4 //
—————————————
255*pi
$$frac{1}{255 pi} left(34 sin{left (frac{15 pi}{4} x right )} – 30 sin{left (frac{17 pi}{4} x right )}right)$$
Комбинаторика
/ /17*pi*x /15*pi*x
2*|- 15*sin|——-| + 17*sin|——-||
4 / 4 //
—————————————
255*pi
$$frac{1}{255 pi} left(34 sin{left (frac{15 pi}{4} x right )} – 30 sin{left (frac{17 pi}{4} x right )}right)$$
Раскрыть выражение
/17*pi*x /15*pi*x
2*sin|——-| 2*sin|——-|
4 / 4 /
– ————– + ————–
17*pi 15*pi
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} x right )} – frac{2}{17 pi} sin{left (frac{17 pi}{4} x right )}$$
/17*pi*x /15*pi*x
2*pi*sin|——-| 2*sin|——-|
4 / 4 /
– —————– + ————–
17 15*pi
$$frac{2}{15 pi} sin{left (frac{15 pi}{4} x right )} – frac{2 pi}{17} sin{left (frac{17 pi}{4} x right )}$$
