Дано
$$frac{1}{231} left(42 sin^{frac{11}{2}}{left (x right )} – 132 sin^{frac{7}{2}}{left (x right )} + 154 sin^{frac{3}{2}}{left (x right )}right)$$
Подстановка условия
$$frac{1}{231} left(42 sin^{frac{11}{2}}{left (x right )} – 132 sin^{frac{7}{2}}{left (x right )} + 154 sin^{frac{3}{2}}{left (x right )}right)$$
(42*sin((1/3))^(11/2) – 132*sin((1/3))^(7/2) + 154*sin((1/3))^(3/2))/231
$$frac{1}{231} left(42 sin^{frac{11}{2}}{left ((1/3) right )} – 132 sin^{frac{7}{2}}{left ((1/3) right )} + 154 sin^{frac{3}{2}}{left ((1/3) right )}right)$$
(42*sin(1/3)^(11/2) – 132*sin(1/3)^(7/2) + 154*sin(1/3)^(3/2))/231
$$frac{1}{231} left(- 132 sin^{frac{7}{2}}{left (frac{1}{3} right )} + 42 sin^{frac{11}{2}}{left (frac{1}{3} right )} + 154 sin^{frac{3}{2}}{left (frac{1}{3} right )}right)$$
-4*sin(1/3)^(7/2)/7 + 2*sin(1/3)^(3/2)/3 + 2*sin(1/3)^(11/2)/11
$$- frac{4}{7} sin^{frac{7}{2}}{left (frac{1}{3} right )} + frac{2}{11} sin^{frac{11}{2}}{left (frac{1}{3} right )} + frac{2}{3} sin^{frac{3}{2}}{left (frac{1}{3} right )}$$
Степени
$$frac{2}{11} sin^{frac{11}{2}}{left (x right )} – frac{4}{7} sin^{frac{7}{2}}{left (x right )} + frac{2}{3} sin^{frac{3}{2}}{left (x right )}$$
Численный ответ
0.181818181818182*sin(x)^5.5 + 0.666666666666667*sin(x)^1.5 – 0.571428571428571*sin(x)^3.5
Рациональный знаменатель
$$frac{2}{11} sin^{frac{11}{2}}{left (x right )} – frac{4}{7} sin^{frac{7}{2}}{left (x right )} + frac{2}{3} sin^{frac{3}{2}}{left (x right )}$$
Объединение рациональных выражений
$$frac{2}{231} left(3 left(7 sin^{2}{left (x right )} – 22right) sin^{2}{left (x right )} + 77right) sin^{frac{3}{2}}{left (x right )}$$
Общее упрощение
3/2 / 2 4
2*sin (x)*77 – 66*sin (x) + 21*sin (x)/
——————————————
231
$$frac{2}{231} left(21 sin^{4}{left (x right )} – 66 sin^{2}{left (x right )} + 77right) sin^{frac{3}{2}}{left (x right )}$$
Соберем выражение
$$frac{2}{11} sin^{frac{11}{2}}{left (x right )} – frac{4}{7} sin^{frac{7}{2}}{left (x right )} + frac{2}{3} sin^{frac{3}{2}}{left (x right )}$$
3/2 11/2 7/2
2*sin (x) 2*sin (x) 132*sin (x)
———– + ———— – ————-
3 11 231
$$frac{2}{11} sin^{frac{11}{2}}{left (x right )} – frac{4}{7} sin^{frac{7}{2}}{left (x right )} + frac{2}{3} sin^{frac{3}{2}}{left (x right )}$$
Общий знаменатель
7/2 3/2 11/2
4*sin (x) 2*sin (x) 2*sin (x)
– ———– + ———– + ————
7 3 11
$$frac{2}{11} sin^{frac{11}{2}}{left (x right )} – frac{4}{7} sin^{frac{7}{2}}{left (x right )} + frac{2}{3} sin^{frac{3}{2}}{left (x right )}$$
Тригонометрическая часть
3/2 / 2 4
2*sin (x)*77 – 66*sin (x) + 21*sin (x)/
——————————————
231
$$frac{2}{231} left(21 sin^{4}{left (x right )} – 66 sin^{2}{left (x right )} + 77right) sin^{frac{3}{2}}{left (x right )}$$
Комбинаторика
3/2 / 2 4
2*sin (x)*77 – 66*sin (x) + 21*sin (x)/
——————————————
231
$$frac{2}{231} left(21 sin^{4}{left (x right )} – 66 sin^{2}{left (x right )} + 77right) sin^{frac{3}{2}}{left (x right )}$$
Раскрыть выражение
7/2 3/2 11/2
4*sin (x) 2*sin (x) 2*sin (x)
– ———– + ———– + ————
7 3 11
$$frac{2}{11} sin^{frac{11}{2}}{left (x right )} – frac{4}{7} sin^{frac{7}{2}}{left (x right )} + frac{2}{3} sin^{frac{3}{2}}{left (x right )}$$
