Господин Экзамен
Другие калькуляторы
-
Как пользоваться?
- sqrt(a+10*sqrt(a-25)) если a=-3
- sin(7*a)-sin(a) если a=-2
- sqrt(4-4*sin(2*a))*sqrt(2-2*cos(2*a)) если a=-1/3
- (7*p+2*q)^2+(7*p-2*q)^2 если q=-4
- Разложить многочлен на множители:
- 2*s-s^2
- x^4-y^4
- 25+x^2
- x^2-11*x+24
- Общий знаменатель:
- (u^2-2*u+4)/(4*u^2-1)*(2*u^2+4)/(u^3+8)
- t/(t+3)^3-3/(t+3)^3
- x^2-49/x^2+9*x*x^2-81/x^2-7*x
- sqrt(2)/(sqrt(8)+2)-((6-sqrt(32))/sqrt(8)-3)
- Умножение столбиком:
- 75*12
- 80*11
- 419*217
- 28*34
- Деление столбиком:
- 25/9
- 91/3
- 95/5
- 1000/9
- Раскрыть скобки в:
- 5*(a-b)+x*(b-a)
- 7*(x+8)+(x+8)*(x-8)
- (3*x-11)*2-5*(4-3*x)
- 7*(a+b)
- Разложение числа на простые множители:
- 31024
- 388
- 4860
- 6652
- График функции y =:
- -2
- Производная:
- -2
- Интеграл d{x}:
-
-2
-
Идентичные выражения
- sin(семь *a)-sin(a) если a=- два
- синус от (7 умножить на a) минус синус от (a) если a равно минус 2
- синус от (семь умножить на a) минус синус от (a) если a равно минус два
- sin(7a)-sin(a) если a=-2
- sin7a-sina если a=-2
- sin(7*a)-sin(a) при a=-2
-
Похожие выражения
- sin(7*a)+sin(a) если a=-2
- sin(7*a)-sin(a) если a=+2
sin(7*a)-sin(a) если a=-2
Решение
Вы ввели
[src]
sin(7*a) - sin(a)
$$- \sin{\left(a \right)} + \sin{\left(7 a \right)}$$
sin(7*a) - sin(a)
Подстановка условия
[src]
sin(7*a) - sin(a) при a = -2
подставляем
sin(7*a) - sin(a)
$$- \sin{\left(a \right)} + \sin{\left(7 a \right)}$$
-sin(a) + sin(7*a)
$$- \sin{\left(a \right)} + \sin{\left(7 a \right)}$$
переменные
a = -2
$$a = -2$$
-sin((-2)) + sin(7*(-2))
$$- \sin{\left((-2) \right)} + \sin{\left(7 (-2) \right)}$$
-sin(-2) + sin(7*-2)
$$\sin{\left(7 \left(-2\right) \right)} - \sin{\left(-2 \right)}$$
-sin(14) + sin(2)
$$- \sin{\left(14 \right)} + \sin{\left(2 \right)}$$
-sin(14) + sin(2)
Степени
[src]
/ -I*a I*a\ / -7*I*a 7*I*a\
I*\- e + e / I*\- e + e /
------------------ - ----------------------
2 2
$$\frac{i \left(e^{i a} - e^{- i a}\right)}{2} - \frac{i \left(e^{7 i a} - e^{- 7 i a}\right)}{2}$$
i*(-exp(-i*a) + exp(i*a))/2 - i*(-exp(-7*i*a) + exp(7*i*a))/2
Тригонометрическая часть
[src]
2*cos(4*a)*sin(3*a)
$$2 \sin{\left(3 a \right)} \cos{\left(4 a \right)}$$
1 1 -------- - ------ csc(7*a) csc(a)
$$\frac{1}{\csc{\left(7 a \right)}} - \frac{1}{\csc{\left(a \right)}}$$
/ pi\ / pi\
- cos|a - --| + cos|7*a - --|
\ 2 / \ 2 /
$$- \cos{\left(a - \frac{\pi}{2} \right)} + \cos{\left(7 a - \frac{\pi}{2} \right)}$$
1 1 ------------- - ----------- csc(pi - 7*a) csc(pi - a)
$$- \frac{1}{\csc{\left(- a + \pi \right)}} + \frac{1}{\csc{\left(- 7 a + \pi \right)}}$$
1 1 ------------- - ----------- / pi\ / pi\ sec|7*a - --| sec|a - --| \ 2 / \ 2 /
$$\frac{1}{\sec{\left(7 a - \frac{\pi}{2} \right)}} - \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}$$
1 1 ------------- - ----------- /pi \ /pi \ sec|-- - 7*a| sec|-- - a| \2 / \2 /
$$- \frac{1}{\sec{\left(- a + \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(- 7 a + \frac{\pi}{2} \right)}}$$
/7*a\ /a\
(1 + cos(7*a))*tan|---| - (1 + cos(a))*tan|-|
\ 2 / \2/
$$- \left(\cos{\left(a \right)} + 1\right) \tan{\left(\frac{a}{2} \right)} + \left(\cos{\left(7 a \right)} + 1\right) \tan{\left(\frac{7 a}{2} \right)}$$
/a\ /7*a\
2*tan|-| 2*tan|---|
\2/ \ 2 /
- ----------- + -------------
2/a\ 2/7*a\
1 + tan |-| 1 + tan |---|
\2/ \ 2 /
$$\frac{2 \tan{\left(\frac{7 a}{2} \right)}}{\tan^{2}{\left(\frac{7 a}{2} \right)} + 1} - \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$
/a\ /7*a\
2*cot|-| 2*cot|---|
\2/ \ 2 /
- ----------- + -------------
2/a\ 2/7*a\
1 + cot |-| 1 + cot |---|
\2/ \ 2 /
$$\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1} - \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}$$
2 2 - -------------------- + ------------------------ / 1 \ /a\ / 1 \ /7*a\ |1 + -------|*cot|-| |1 + ---------|*cot|---| | 2/a\| \2/ | 2/7*a\| \ 2 / | cot |-|| | cot |---|| \ \2// \ \ 2 //
$$\frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{7 a}{2} \right)}}\right) \cot{\left(\frac{7 a}{2} \right)}} - \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(\frac{a}{2} \right)}}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ - |< | + |< | \\sin(a) otherwise / \\sin(7*a) otherwise /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\sin{\left(7 a \right)} & \text{otherwise} \end{cases}\right)$$
2/pi 7*a\ 2/a pi\
-1 + tan |-- + ---| -1 + tan |- + --|
\4 2 / \2 4 /
------------------- - -----------------
2/pi 7*a\ 2/a pi\
1 + tan |-- + ---| 1 + tan |- + --|
\4 2 / \2 4 /
$$- \frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} + \frac{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1}$$
/ 2/pi 7*a\\ / 2/a pi\\
|1 - cot |-- + ---||*(1 + sin(7*a)) |1 - cot |- + --||*(1 + sin(a))
\ \4 2 // \ \2 4 //
----------------------------------- - -------------------------------
2 2
$$- \frac{\left(- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(a \right)} + 1\right)}{2} + \frac{\left(- \cot^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(7 a \right)} + 1\right)}{2}$$
2/pi 7*a\ 2/a pi\
1 - cot |-- + ---| 1 - cot |- + --|
\4 2 / \2 4 /
------------------ - ----------------
2/pi 7*a\ 2/a pi\
1 + cot |-- + ---| 1 + cot |- + --|
\4 2 / \2 4 /
$$- \frac{- \cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} + \frac{- \cot^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | - |< 1 | + |< 1 | ||------ otherwise | ||-------- otherwise | \\csc(a) / \\csc(7*a) /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\csc{\left(a \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{1}{\csc{\left(7 a \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | - |< / pi\ | + |< / pi\ | ||cos|a - --| otherwise | ||cos|7*a - --| otherwise | \\ \ 2 / / \\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\cos{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\cos{\left(7 a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right)$$
2/a\ 2/7*a\
4*sin |-|*sin(a) 4*sin |---|*sin(7*a)
\2/ \ 2 /
- ------------------- + -----------------------
2 4/a\ 2 4/7*a\
sin (a) + 4*sin |-| sin (7*a) + 4*sin |---|
\2/ \ 2 /
$$\frac{4 \sin^{2}{\left(\frac{7 a}{2} \right)} \sin{\left(7 a \right)}}{4 \sin^{4}{\left(\frac{7 a}{2} \right)} + \sin^{2}{\left(7 a \right)}} - \frac{4 \sin^{2}{\left(\frac{a}{2} \right)} \sin{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)} + \sin^{2}{\left(a \right)}}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || 1 | || 1 | - |<----------- otherwise | + |<------------- otherwise | || / pi\ | || / pi\ | ||sec|a - --| | ||sec|7*a - --| | \\ \ 2 / / \\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{1}{\sec{\left(7 a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// / 3*pi\ \ // / 3*pi\ \ || 1 for |a + ----| mod 2*pi = 0| || 1 for |7*a + ----| mod 2*pi = 0| - |< \ 2 / | + |< \ 2 / | || | || | \\sin(a) otherwise / \\sin(7*a) otherwise /
$$\left(- \begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(7 a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(7 a \right)} & \text{otherwise} \end{cases}\right)$$
2/a\ 2/7*a\
4*sin |-| 4*sin |---|
\2/ \ 2 /
- ---------------------- + --------------------------
/ 4/a\\ / 4/7*a\\
| 4*sin |-|| | 4*sin |---||
| \2/| | \ 2 /|
|1 + ---------|*sin(a) |1 + -----------|*sin(7*a)
| 2 | | 2 |
\ sin (a) / \ sin (7*a) /
$$\frac{4 \sin^{2}{\left(\frac{7 a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{7 a}{2} \right)}}{\sin^{2}{\left(7 a \right)}} + 1\right) \sin{\left(7 a \right)}} - \frac{4 \sin^{2}{\left(\frac{a}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{a}{2} \right)}}{\sin^{2}{\left(a \right)}} + 1\right) \sin{\left(a \right)}}$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | ||1 - cos(a) | ||1 - cos(7*a) | - |<---------- otherwise | + |<------------ otherwise | || /a\ | || /7*a\ | || tan|-| | || tan|---| | \\ \2/ / \\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{- \cos{\left(a \right)} + 1}{\tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{- \cos{\left(7 a \right)} + 1}{\tan{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || /a\ | || /7*a\ | || 2*tan|-| | || 2*tan|---| | - |< \2/ | + |< \ 2 / | ||----------- otherwise | ||------------- otherwise | || 2/a\ | || 2/7*a\ | ||1 + tan |-| | ||1 + tan |---| | \\ \2/ / \\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{7 a}{2} \right)}}{\tan^{2}{\left(\frac{7 a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || /a\ | || /7*a\ | || 2*cot|-| | || 2*cot|---| | - |< \2/ | + |< \ 2 / | ||----------- otherwise | ||------------- otherwise | || 2/a\ | || 2/7*a\ | ||1 + cot |-| | ||1 + cot |---| | \\ \2/ / \\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
- |
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\sin{\left(7 a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| 2 | || 2 |
||-------------------- otherwise | ||------------------------ otherwise |
- |
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{7 a}{2} \right)}}\right) \tan{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
/a\ /7*a\
2*sec|-| 2*sec|---|
\2/ \ 2 /
- ------------------------------ + --------------------------------------
/ 2/a\ \ / 2/7*a\ \
| sec |-| | | sec |---| |
| \2/ | /a pi\ | \ 2 / | / pi 7*a\
|1 + ------------|*sec|- - --| |1 + ----------------|*sec|- -- + ---|
| 2/a pi\| \2 2 / | 2/ pi 7*a\| \ 2 2 /
| sec |- - --|| | sec |- -- + ---||
\ \2 2 // \ \ 2 2 //
$$\frac{2 \sec{\left(\frac{7 a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{7 a}{2} \right)}}{\sec^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} - \frac{2 \sec{\left(\frac{a}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{a}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}$$
/a pi\ / pi 7*a\
2*cos|- - --| 2*cos|- -- + ---|
\2 2 / \ 2 2 /
- ------------------------- + -------------------------------
/ 2/a pi\\ / 2/ pi 7*a\\
| cos |- - --|| | cos |- -- + ---||
| \2 2 /| /a\ | \ 2 2 /| /7*a\
|1 + ------------|*cos|-| |1 + ----------------|*cos|---|
| 2/a\ | \2/ | 2/7*a\ | \ 2 /
| cos |-| | | cos |---| |
\ \2/ / \ \ 2 / /
$$\frac{2 \cos{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{7 a}{2} \right)}}\right) \cos{\left(\frac{7 a}{2} \right)}} - \frac{2 \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} \right)}}\right) \cos{\left(\frac{a}{2} \right)}}$$
/pi a\ /pi 7*a\
2*csc|-- - -| 2*csc|-- - ---|
\2 2/ \2 2 /
- ------------------------- + -----------------------------
/ 2/pi a\\ / 2/pi 7*a\\
| csc |-- - -|| | csc |-- - ---||
| \2 2/| /a\ | \2 2 /| /7*a\
|1 + ------------|*csc|-| |1 + --------------|*csc|---|
| 2/a\ | \2/ | 2/7*a\ | \ 2 /
| csc |-| | | csc |---| |
\ \2/ / \ \ 2 / /
$$\frac{2 \csc{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{7 a}{2} \right)}}\right) \csc{\left(\frac{7 a}{2} \right)}} - \frac{2 \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{a}{2} \right)}}\right) \csc{\left(\frac{a}{2} \right)}}$$
// 0 for a mod pi = 0\ || | || 2*sin(a) | // 0 for 7*a mod pi = 0\ ||---------------------------- otherwise | || | || / 2 \ | || -2*sin(14*a) + 4*sin(7*a) | - |< | sin (a) | | + |<--------------------------------- otherwise | ||(1 - cos(a))*|1 + ---------| | || 2 | || | 4/a\| | ||1 - cos(14*a) + 2*(1 - cos(7*a)) | || | 4*sin |-|| | \\ / || \ \2// | \\ /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \left(- \cos{\left(a \right)} + 1\right)} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{4 \sin{\left(7 a \right)} - 2 \sin{\left(14 a \right)}}{2 \left(- \cos{\left(7 a \right)} + 1\right)^{2} - \cos{\left(14 a \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// / 3*pi\ \ // / 3*pi\ \ || 1 for |a + ----| mod 2*pi = 0| || 1 for |7*a + ----| mod 2*pi = 0| || \ 2 / | || \ 2 / | || | || | || 2/a pi\ | || 2/pi 7*a\ | - |<-1 + tan |- + --| | + |<-1 + tan |-- + ---| | || \2 4 / | || \4 2 / | ||----------------- otherwise | ||------------------- otherwise | || 2/a pi\ | || 2/pi 7*a\ | || 1 + tan |- + --| | || 1 + tan |-- + ---| | \\ \2 4 / / \\ \4 2 / /
$$\left(- \begin{cases} 1 & \text{for}\: \left(a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 1 & \text{for}\: \left(7 a + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{7 a}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | || sin(a) | || sin(7*a) | ||----------------------- otherwise | ||--------------------------- otherwise | ||/ 2 \ | ||/ 2 \ | - |<| sin (a) | 2/a\ | + |<| sin (7*a) | 2/7*a\ | |||1 + ---------|*sin |-| | |||1 + -----------|*sin |---| | ||| 4/a\| \2/ | ||| 4/7*a\| \ 2 / | ||| 4*sin |-|| | ||| 4*sin |---|| | ||\ \2// | ||\ \ 2 // | \\ / \\ /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{\sin{\left(a \right)}}{\left(1 + \frac{\sin^{2}{\left(a \right)}}{4 \sin^{4}{\left(\frac{a}{2} \right)}}\right) \sin^{2}{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{\sin{\left(7 a \right)}}{\left(1 + \frac{\sin^{2}{\left(7 a \right)}}{4 \sin^{4}{\left(\frac{7 a}{2} \right)}}\right) \sin^{2}{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\ || | || | ||/ 0 for a mod pi = 0 | ||/ 0 for 7*a mod pi = 0 | ||| | ||| | ||| /a\ | ||| /7*a\ | - |<| 2*cot|-| | + |<| 2*cot|---| | ||< \2/ otherwise | ||< \ 2 / otherwise | |||----------- otherwise | |||------------- otherwise | ||| 2/a\ | ||| 2/7*a\ | |||1 + cot |-| | |||1 + cot |---| | \\\ \2/ / \\\ \ 2 / /
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{7 a}{2} \right)}}{\cot^{2}{\left(\frac{7 a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| /a\ | || /7*a\ |
|| 2*cos|-| | || 2*cos|---| |
|| \2/ | || \ 2 / |
||------------------------------ otherwise | ||-------------------------------------- otherwise |
- |
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{a}{2} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{7 a}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{7 a}{2} \right)}}{\cos^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| /a pi\ | || / pi 7*a\ |
|| 2*sec|- - --| | || 2*sec|- -- + ---| |
|| \2 2 / | || \ 2 2 / |
||------------------------- otherwise | ||------------------------------- otherwise |
- |
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{a}{2} \right)}}\right) \sec{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{7 a}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{7 a}{2} \right)}}\right) \sec{\left(\frac{7 a}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
// 0 for a mod pi = 0\ // 0 for 7*a mod pi = 0\
|| | || |
|| /a\ | || /7*a\ |
|| 2*csc|-| | || 2*csc|---| |
|| \2/ | || \ 2 / |
||------------------------------ otherwise | ||---------------------------------- otherwise |
- |
$$\left(- \begin{cases} 0 & \text{for}\: a \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{a}{2} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) + \left(\begin{cases} 0 & \text{for}\: 7 a \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{7 a}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{7 a}{2} \right)}}{\csc^{2}{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{7 a}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right)$$
-Piecewise((0, Mod(a = pi, 0)), (2*csc(a/2)/((1 + csc(a/2)^2/csc(pi/2 - a/2)^2)*csc(pi/2 - a/2)), True)) + Piecewise((0, Mod(7*a = pi, 0)), (2*csc(7*a/2)/((1 + csc(7*a/2)^2/csc(pi/2 - 7*a/2)^2)*csc(pi/2 - 7*a/2)), True))