2*sin(22*x)+4+2*cos(22*x) если x=-2 (упростите выражение)

Вы ввели

2*sin(22*x) + 4 + 2*cos(22*x)

$$2 \sin{\left (22 x \right )} + 4 + 2 \cos{\left (22 x \right )}$$

Подстановка условия

2*sin(22*x) + 4 + 2*cos(22*x) при x = -2

2*sin(22*x) + 4 + 2*cos(22*x)

$$2 \sin{\left (22 x \right )} + 4 + 2 \cos{\left (22 x \right )}$$

2*sin(22*(-2)) + 4 + 2*cos(22*(-2))

$$2 \sin{\left (22 (-2) \right )} + 4 + 2 \cos{\left (22 (-2) \right )}$$

2*sin(22*(-2)) + 4 + 2*cos(22*(-2))

$$2 \cos{\left (-2 \cdot 22 \right )} + 2 \sin{\left (-2 \cdot 22 \right )} + 4$$

4 - 2*sin(44) + 2*cos(44)

$$- 2 \sin{\left (44 \right )} + 2 \cos{\left (44 \right )} + 4$$

Степени

4 + 2*cos(22*x) + 2*sin(22*x)

$$2 \sin{\left (22 x \right )} + 2 \cos{\left (22 x \right )} + 4$$

Численный ответ

4.0 + 2.0*cos(22*x) + 2.0*sin(22*x)

Рациональный знаменатель

4 + 2*cos(22*x) + 2*sin(22*x)

$$2 \sin{\left (22 x \right )} + 2 \cos{\left (22 x \right )} + 4$$

Объединение рациональных выражений

2*(2 + cos(22*x) + sin(22*x))

$$2 \left(\sin{\left (22 x \right )} + \cos{\left (22 x \right )} + 2\right)$$

Общее упрощение

        ___    /       pi\
4 + 2*\/ 2 *sin|22*x + --|
               \       4 /

$$2 \sqrt{2} \sin{\left (22 x + \frac{\pi}{4} \right )} + 4$$

Собрать выражение

4 + 2*cos(22*x) + 2*sin(22*x)

$$2 \sin{\left (22 x \right )} + 2 \cos{\left (22 x \right )} + 4$$

Комбинаторика

2*(2 + cos(22*x) + sin(22*x))

$$2 \left(\sin{\left (22 x \right )} + \cos{\left (22 x \right )} + 2\right)$$

Общий знаменатель

4 + 2*cos(22*x) + 2*sin(22*x)

$$2 \sin{\left (22 x \right )} + 2 \cos{\left (22 x \right )} + 4$$

Тригонометрическая часть

        ___    /       pi\
4 + 2*\/ 2 *sin|22*x + --|
               \       4 /

$$2 \sqrt{2} \sin{\left (22 x + \frac{\pi}{4} \right )} + 4$$

Раскрыть выражение

         22           22                 11       11                 12       10                8       14                7       15                15       7                16       6               4       18              3       19              19       3             20       2            21                   21                    2       20               18       4               5       17               17       5                6       16                14       8                9       13                13       9                 10       12   
4 - 2*sin  (x) + 2*cos  (x) - 1410864*cos  (x)*sin  (x) - 1293292*cos  (x)*sin  (x) - 639540*cos (x)*sin  (x) - 341088*cos (x)*sin  (x) - 341088*cos  (x)*sin (x) - 149226*cos  (x)*sin (x) - 14630*cos (x)*sin  (x) - 3080*cos (x)*sin  (x) - 3080*cos  (x)*sin (x) - 462*cos  (x)*sin (x) + 44*cos  (x)*sin(x) + 44*sin  (x)*cos(x) + 462*cos (x)*sin  (x) + 14630*cos  (x)*sin (x) + 52668*cos (x)*sin  (x) + 52668*cos  (x)*sin (x) + 149226*cos (x)*sin  (x) + 639540*cos  (x)*sin (x) + 994840*cos (x)*sin  (x) + 994840*cos  (x)*sin (x) + 1293292*cos  (x)*sin  (x)

$$- 2 \sin^{22}{\left (x \right )} + 44 \sin^{21}{\left (x \right )} \cos{\left (x \right )} + 462 \sin^{20}{\left (x \right )} \cos^{2}{\left (x \right )} - 3080 \sin^{19}{\left (x \right )} \cos^{3}{\left (x \right )} - 14630 \sin^{18}{\left (x \right )} \cos^{4}{\left (x \right )} + 52668 \sin^{17}{\left (x \right )} \cos^{5}{\left (x \right )} + 149226 \sin^{16}{\left (x \right )} \cos^{6}{\left (x \right )} - 341088 \sin^{15}{\left (x \right )} \cos^{7}{\left (x \right )} - 639540 \sin^{14}{\left (x \right )} \cos^{8}{\left (x \right )} + 994840 \sin^{13}{\left (x \right )} \cos^{9}{\left (x \right )} + 1293292 \sin^{12}{\left (x \right )} \cos^{10}{\left (x \right )} - 1410864 \sin^{11}{\left (x \right )} \cos^{11}{\left (x \right )} - 1293292 \sin^{10}{\left (x \right )} \cos^{12}{\left (x \right )} + 994840 \sin^{9}{\left (x \right )} \cos^{13}{\left (x \right )} + 639540 \sin^{8}{\left (x \right )} \cos^{14}{\left (x \right )} - 341088 \sin^{7}{\left (x \right )} \cos^{15}{\left (x \right )} - 149226 \sin^{6}{\left (x \right )} \cos^{16}{\left (x \right )} + 52668 \sin^{5}{\left (x \right )} \cos^{17}{\left (x \right )} + 14630 \sin^{4}{\left (x \right )} \cos^{18}{\left (x \right )} - 3080 \sin^{3}{\left (x \right )} \cos^{19}{\left (x \right )} - 462 \sin^{2}{\left (x \right )} \cos^{20}{\left (x \right )} + 44 \sin{\left (x \right )} \cos^{21}{\left (x \right )} + 2 \cos^{22}{\left (x \right )} + 4$$