Тригонометрическая часть
[src]
$$- \cos^{2}{\left(7 y \right)}$$
$$- \frac{1}{\sec^{2}{\left(7 y \right)}}$$
1
-1 + ---------
2
csc (7*y)
$$-1 + \frac{1}{\csc^{2}{\left(7 y \right)}}$$
2/pi \
-sin |-- + 7*y|
\2 /
$$- \sin^{2}{\left(7 y + \frac{\pi}{2} \right)}$$
2/ pi\
-1 + cos |7*y - --|
\ 2 /
$$\cos^{2}{\left(7 y - \frac{\pi}{2} \right)} - 1$$
1 cos(14*y)
- - - ---------
2 2
$$- \frac{\cos{\left(14 y \right)}}{2} - \frac{1}{2}$$
1
-1 + --------------
2
csc (pi - 7*y)
$$-1 + \frac{1}{\csc^{2}{\left(- 7 y + \pi \right)}}$$
-1
--------------
2/pi \
csc |-- - 7*y|
\2 /
$$- \frac{1}{\csc^{2}{\left(- 7 y + \frac{\pi}{2} \right)}}$$
1
-1 + --------------
2/ pi\
sec |7*y - --|
\ 2 /
$$-1 + \frac{1}{\sec^{2}{\left(7 y - \frac{\pi}{2} \right)}}$$
1
-1 + --------------
2/pi \
sec |-- - 7*y|
\2 /
$$-1 + \frac{1}{\sec^{2}{\left(- 7 y + \frac{\pi}{2} \right)}}$$
2 2
1 sin (7*y) cos (7*y)
- - + --------- - ---------
2 2 2
$$\frac{\sin^{2}{\left(7 y \right)}}{2} - \frac{\cos^{2}{\left(7 y \right)}}{2} - \frac{1}{2}$$
2/7*y\
4*cot |---|
\ 2 /
-1 + ----------------
2
/ 2/7*y\\
|1 + cot |---||
\ \ 2 //
$$-1 + \frac{4 \cot^{2}{\left(\frac{7 y}{2} \right)}}{\left(\cot^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}}$$
2/7*y\
4*tan |---|
\ 2 /
-1 + ----------------
2
/ 2/7*y\\
|1 + tan |---||
\ \ 2 //
$$-1 + \frac{4 \tan^{2}{\left(\frac{7 y}{2} \right)}}{\left(\tan^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}}$$
// 1 for 7*y mod 2*pi = 0\
|| |
-|< 2 |
||cos (7*y) otherwise |
\\ /
$$- \begin{cases} 1 & \text{for}\: 7 y \bmod 2 \pi = 0 \\\cos^{2}{\left(7 y \right)} & \text{otherwise} \end{cases}$$
4
-1 + --------------------------
2
/ 1 \ 2/7*y\
|1 + ---------| *cot |---|
| 2/7*y\| \ 2 /
| cot |---||
\ \ 2 //
$$-1 + \frac{4}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{7 y}{2} \right)}}\right)^{2} \cot^{2}{\left(\frac{7 y}{2} \right)}}$$
// 0 for 7*y mod pi = 0\
|| |
-1 + |< 2 |
||sin (7*y) otherwise |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\sin^{2}{\left(7 y \right)} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 2/7*y\\
-|1 - tan |---||
\ \ 2 //
------------------
2
/ 2/7*y\\
|1 + tan |---||
\ \ 2 //
$$- \frac{\left(- \tan^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}}{\left(\tan^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}}$$
// 0 for 7*y mod pi = 0\
|| |
|| 1 |
-1 + |<--------- otherwise |
|| 2 |
||csc (7*y) |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{1}{\csc^{2}{\left(7 y \right)}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
-1 + |< 2/ pi\ |
||cos |7*y - --| otherwise |
\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\cos^{2}{\left(7 y - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
|| 1 |
-1 + |<-------------- otherwise |
|| 2/ pi\ |
||sec |7*y - --| |
\\ \ 2 / /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{1}{\sec^{2}{\left(7 y - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
2
/ 2/pi 7*y\\
|-1 + tan |-- + ---||
\ \4 2 //
-1 + ----------------------
2
/ 2/pi 7*y\\
|1 + tan |-- + ---||
\ \4 2 //
$$\frac{\left(\tan^{2}{\left(\frac{7 y}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{7 y}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} - 1$$
2
/ 2/pi 7*y\\
|1 - cot |-- + ---||
\ \4 2 //
-1 + ---------------------
2
/ 2/pi 7*y\\
|1 + cot |-- + ---||
\ \4 2 //
$$\frac{\left(- \cot^{2}{\left(\frac{7 y}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{7 y}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} - 1$$
2 4/7*y\
16*sin (7*y)*sin |---|
\ 2 /
-1 + --------------------------
2
/ 2 4/7*y\\
|sin (7*y) + 4*sin |---||
\ \ 2 //
$$\frac{16 \sin^{4}{\left(\frac{7 y}{2} \right)} \sin^{2}{\left(7 y \right)}}{\left(4 \sin^{4}{\left(\frac{7 y}{2} \right)} + \sin^{2}{\left(7 y \right)}\right)^{2}} - 1$$
4/7*y\
16*sin |---|
\ 2 /
-1 + ----------------------------
2
/ 4/7*y\\
| 4*sin |---||
| \ 2 /| 2
|1 + -----------| *sin (7*y)
| 2 |
\ sin (7*y) /
$$-1 + \frac{16 \sin^{4}{\left(\frac{7 y}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{7 y}{2} \right)}}{\sin^{2}{\left(7 y \right)}} + 1\right)^{2} \sin^{2}{\left(7 y \right)}}$$
// 0 for 7*y mod pi = 0\
|| |
|| 2/7*y\ |
|| 4*tan |---| |
|| \ 2 / |
-1 + |<---------------- otherwise |
|| 2 |
||/ 2/7*y\\ |
|||1 + tan |---|| |
||\ \ 2 // |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4 \tan^{2}{\left(\frac{7 y}{2} \right)}}{\left(\tan^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
|| 2/7*y\ |
|| 4*cot |---| |
|| \ 2 / |
-1 + |<---------------- otherwise |
|| 2 |
||/ 2/7*y\\ |
|||1 + cot |---|| |
||\ \ 2 // |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{7 y}{2} \right)}}{\left(\cot^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
||/ 0 for 7*y mod pi = 0 |
-1 + |<| |
||< 2 otherwise |
|||sin (7*y) otherwise |
\\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\sin^{2}{\left(7 y \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) - 1$$
// 1 for 7*y mod 2*pi = 0\
|| |
|| 2 |
||/ 2/7*y\\ |
|||-1 + cot |---|| |
-|<\ \ 2 // |
||----------------- otherwise |
|| 2 |
|| / 2/7*y\\ |
|| |1 + cot |---|| |
\\ \ \ 2 // /
$$- \begin{cases} 1 & \text{for}\: 7 y \bmod 2 \pi = 0 \\\frac{\left(\cot^{2}{\left(\frac{7 y}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}$$
// / 3*pi\ \
|| 1 for |7*y + ----| mod 2*pi = 0|
|| \ 2 / |
-1 + |< |
|| 4/7*y\ 2/7*y\ |
||- 4*cos |---| + 4*cos |---| otherwise |
\\ \ 2 / \ 2 / /
$$\left(\begin{cases} 1 & \text{for}\: \left(7 y + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\- 4 \cos^{4}{\left(\frac{7 y}{2} \right)} + 4 \cos^{2}{\left(\frac{7 y}{2} \right)} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
|| 4 |
||-------------------------- otherwise |
|| 2 |
-1 + | 1 \ 2/7*y\ |
|||1 + ---------| *tan |---| |
||| 2/7*y\| \ 2 / |
||| tan |---|| |
||\ \ 2 // |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{7 y}{2} \right)}}\right)^{2} \tan^{2}{\left(\frac{7 y}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
2/7*y\
4*sec |---|
\ 2 /
-1 + ----------------------------------------
2
/ 2/7*y\ \
| sec |---| |
| \ 2 / | 2/ pi 7*y\
|1 + ----------------| *sec |- -- + ---|
| 2/ pi 7*y\| \ 2 2 /
| sec |- -- + ---||
\ \ 2 2 //
$$-1 + \frac{4 \sec^{2}{\left(\frac{7 y}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{7 y}{2} \right)}}{\sec^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \sec^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}}$$
2/ pi 7*y\
4*cos |- -- + ---|
\ 2 2 /
-1 + ---------------------------------
2
/ 2/ pi 7*y\\
| cos |- -- + ---||
| \ 2 2 /| 2/7*y\
|1 + ----------------| *cos |---|
| 2/7*y\ | \ 2 /
| cos |---| |
\ \ 2 / /
$$-1 + \frac{4 \cos^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{7 y}{2} \right)}}\right)^{2} \cos^{2}{\left(\frac{7 y}{2} \right)}}$$
2/pi 7*y\
4*csc |-- - ---|
\2 2 /
-1 + -------------------------------
2
/ 2/pi 7*y\\
| csc |-- - ---||
| \2 2 /| 2/7*y\
|1 + --------------| *csc |---|
| 2/7*y\ | \ 2 /
| csc |---| |
\ \ 2 / /
$$-1 + \frac{4 \csc^{2}{\left(- \frac{7 y}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{7 y}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{7 y}{2} \right)}}\right)^{2} \csc^{2}{\left(\frac{7 y}{2} \right)}}$$
// 0 for 7*y mod pi = 0\
|| |
|| 2 |
|| sin (7*y) |
||---------------------------- otherwise |
|| 2 |
-1 + | 2 \ |
||| sin (7*y) | 4/7*y\ |
|||1 + -----------| *sin |---| |
||| 4/7*y\| \ 2 / |
||| 4*sin |---|| |
||\ \ 2 // |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{\sin^{2}{\left(7 y \right)}}{\left(1 + \frac{\sin^{2}{\left(7 y \right)}}{4 \sin^{4}{\left(\frac{7 y}{2} \right)}}\right)^{2} \sin^{4}{\left(\frac{7 y}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
||/ 0 for 7*y mod pi = 0 |
||| |
||| 2/7*y\ |
||| 4*cot |---| |
-1 + |<| \ 2 / |
||<---------------- otherwise otherwise |
||| 2 |
|||/ 2/7*y\\ |
||||1 + cot |---|| |
|||\ \ 2 // |
\\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{7 y}{2} \right)}}{\left(\cot^{2}{\left(\frac{7 y}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right) - 1$$
// / 3*pi\ \
|| 1 for |7*y + ----| mod 2*pi = 0|
|| \ 2 / |
|| |
|| 2 |
||/ 2/pi 7*y\\ |
-1 + |<|-1 + tan |-- + ---|| |
||\ \4 2 // |
||---------------------- otherwise |
|| 2 |
||/ 2/pi 7*y\\ |
|||1 + tan |-- + ---|| |
\\\ \4 2 // /
$$\left(\begin{cases} 1 & \text{for}\: \left(7 y + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\left(\tan^{2}{\left(\frac{7 y}{2} + \frac{\pi}{4} \right)} - 1\right)^{2}}{\left(\tan^{2}{\left(\frac{7 y}{2} + \frac{\pi}{4} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
|| 2/ pi 7*y\ |
|| 4*sec |- -- + ---| |
|| \ 2 2 / |
||--------------------------------- otherwise |
|| 2 |
-1 + | 2/ pi 7*y\\ |
||| sec |- -- + ---|| |
||| \ 2 2 /| 2/7*y\ |
|||1 + ----------------| *sec |---| |
||| 2/7*y\ | \ 2 / |
||| sec |---| | |
||\ \ 2 / / |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4 \sec^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{7 y}{2} \right)}}\right)^{2} \sec^{2}{\left(\frac{7 y}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
|| 2/7*y\ |
|| 4*cos |---| |
|| \ 2 / |
||---------------------------------------- otherwise |
|| 2 |
-1 + | 2/7*y\ \ |
||| cos |---| | |
||| \ 2 / | 2/ pi 7*y\ |
|||1 + ----------------| *cos |- -- + ---| |
||| 2/ pi 7*y\| \ 2 2 / |
||| cos |- -- + ---|| |
||\ \ 2 2 // |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4 \cos^{2}{\left(\frac{7 y}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{7 y}{2} \right)}}{\cos^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}} + 1\right)^{2} \cos^{2}{\left(\frac{7 y}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
// 0 for 7*y mod pi = 0\
|| |
|| 2/7*y\ |
|| 4*csc |---| |
|| \ 2 / |
||------------------------------------ otherwise |
|| 2 |
-1 + | 2/7*y\ \ |
||| csc |---| | |
||| \ 2 / | 2/pi 7*y\ |
|||1 + --------------| *csc |-- - ---| |
||| 2/pi 7*y\| \2 2 / |
||| csc |-- - ---|| |
||\ \2 2 // |
\\ /
$$\left(\begin{cases} 0 & \text{for}\: 7 y \bmod \pi = 0 \\\frac{4 \csc^{2}{\left(\frac{7 y}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{7 y}{2} \right)}}{\csc^{2}{\left(- \frac{7 y}{2} + \frac{\pi}{2} \right)}} + 1\right)^{2} \csc^{2}{\left(- \frac{7 y}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}\right) - 1$$
-1 + Piecewise((0, Mod(7*y = pi, 0)), (4*csc(7*y/2)^2/((1 + csc(7*y/2)^2/csc(pi/2 - 7*y/2)^2)^2*csc(pi/2 - 7*y/2)^2), True))