Дано

$$frac{1}{768} left(- -1 cdot 120 x + – 16 sin{left (6 x right )} – 3 sin{left (8 x right )} – 24 sin{left (4 x right )} – – 48 sin{left (2 x right )}right)$$
Подстановка условия
$$frac{1}{768} left(- -1 cdot 120 x + – 16 sin{left (6 x right )} – 3 sin{left (8 x right )} – 24 sin{left (4 x right )} – – 48 sin{left (2 x right )}right)$$

(-3*sin(8*(-3)) – 16*sin(6*(-3)) – 24*sin(4*(-3)) – (-1)*48*sin(2*(-3)) – (-1)*120*(-3))/768

$$frac{1}{768} left(- -1 cdot 120 (-3) + – 16 sin{left (6 (-3) right )} – 3 sin{left (8 (-3) right )} – 24 sin{left (4 (-3) right )} – – 48 sin{left (2 (-3) right )}right)$$

(-3*sin(8*(-3)) – 16*sin(6*(-3)) – 24*sin(4*(-3)) – (-1)*48*sin(2*(-3)) – (-1)*120*(-3))/768

$$frac{1}{768} left(- 360 + – 16 sin{left (-3 cdot 6 right )} – 3 sin{left (-3 cdot 8 right )} – 24 sin{left (-3 cdot 4 right )} – – 48 sin{left (-3 cdot 2 right )}right)$$

-15/32 – sin(6)/16 + sin(12)/32 + sin(18)/48 + sin(24)/256

$$- frac{15}{32} + frac{1}{32} sin{left (12 right )} + frac{1}{48} sin{left (18 right )} + frac{1}{256} sin{left (24 right )} – frac{1}{16} sin{left (6 right )}$$
Степени
$$frac{5 x}{32} + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Численный ответ

0.0625*sin(2*x) + 0.15625*x – 0.00390625*sin(8*x) – 0.03125*sin(4*x) – 0.0208333333333333*sin(6*x)

Рациональный знаменатель
$$frac{5 x}{32} + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Объединение рациональных выражений
$$frac{5 x}{32} + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Общее упрощение

sin(4*x) sin(6*x) sin(8*x) sin(2*x) 5*x
– ——– – ——– – ——– + ——– + —
32 48 256 16 32

$$frac{5 x}{32} + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Соберем выражение
$$- frac{1}{32} left(-1 cdot 5 xright) – – frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$

sin(4*x) sin(6*x) sin(8*x) sin(2*x) 5*x
– ——– – ——– – ——– + ——– + —
32 48 256 16 32

$$frac{5 x}{32} + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Общий знаменатель

sin(4*x) sin(6*x) sin(8*x) sin(2*x) 5*x
– ——– – ——– – ——– + ——– + —
32 48 256 16 32

$$frac{5 x}{32} + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Тригонометрическая часть

sin(4*x) sin(6*x) sin(8*x) sin(2*x) -120*x
– ——– – ——– – ——– + ——– – ——-
32 48 256 16 768

$$- frac{1}{32} left(-1 cdot 5 xright) + frac{1}{16} sin{left (2 x right )} – frac{1}{32} sin{left (4 x right )} – frac{1}{48} sin{left (6 x right )} – frac{1}{256} sin{left (8 x right )}$$
Комбинаторика

-24*sin(4*x) – 16*sin(6*x) – 3*sin(8*x) + 48*sin(2*x) + 120*x
————————————————————-
768

$$frac{1}{768} left(120 x + 48 sin{left (2 x right )} – 24 sin{left (4 x right )} – 16 sin{left (6 x right )} – 3 sin{left (8 x right )}right)$$
Раскрыть выражение

3 5 3 5 5 7 3 7 3 3 5 3
5*x 7*cos (x)*sin (x) cos (x)*sin(x) cos (x)*sin(x) sin (x)*cos(x) cos (x)*sin(x) sin (x)*cos(x) cos(x)*sin(x) sin (x)*cos(x) 5*cos (x)*sin (x) 7*cos (x)*sin (x)
— – —————– – ————– – ————– – ————– – ————– + ————– + ————- + ————– + —————– + —————–
32 32 8 8 8 32 8 8 32 12 32

$$frac{5 x}{32} + frac{1}{32} sin^{7}{left (x right )} cos{left (x right )} – frac{7}{32} sin^{5}{left (x right )} cos^{3}{left (x right )} – frac{1}{8} sin^{5}{left (x right )} cos{left (x right )} + frac{7}{32} sin^{3}{left (x right )} cos^{5}{left (x right )} + frac{5}{12} sin^{3}{left (x right )} cos^{3}{left (x right )} + frac{1}{8} sin^{3}{left (x right )} cos{left (x right )} – frac{1}{32} sin{left (x right )} cos^{7}{left (x right )} – frac{1}{8} sin{left (x right )} cos^{5}{left (x right )} – frac{1}{8} sin{left (x right )} cos^{3}{left (x right )} + frac{1}{8} sin{left (x right )} cos{left (x right )}$$
   
4.17
sargy
Магистр технического университета по специальности "Автоматизация техологических процессов" Стаж написания работ онлайн: - курсовых работ - 1 год; - контрольных работ - 2 года; - решение задач - 4 года; - написание рефератов - 5 лет.