Тригонометрическая часть
[src]
/ pi\
2*cos|a + --|
\ 6 /
$$2 \cos{\left(a + \frac{\pi}{6} \right)}$$
/ 2*pi\
2*sin|a + ----|
\ 3 /
$$2 \sin{\left(a + \frac{2 \pi}{3} \right)}$$
2
-----------
/ pi\
sec|a + --|
\ 6 /
$$\frac{2}{\sec{\left(a + \frac{\pi}{6} \right)}}$$
2
------------
/ pi\
csc|-a + --|
\ 3 /
$$\frac{2}{\csc{\left(- a + \frac{\pi}{3} \right)}}$$
___
-sin(a) + \/ 3 *cos(a)
$$- \sin{\left(a \right)} + \sqrt{3} \cos{\left(a \right)}$$
/a pi\
4*tan|- + --|
\2 3 /
----------------
2/a pi\
1 + tan |- + --|
\2 3 /
$$\frac{4 \tan{\left(\frac{a}{2} + \frac{\pi}{3} \right)}}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{3} \right)} + 1}$$
/ 2/a pi\\
2*|-1 + cot |- + --||
\ \2 12//
---------------------
2/a pi\
1 + cot |- + --|
\2 12/
$$\frac{2 \left(\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} - 1\right)}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1}$$
/ 2/a pi\\
2*|1 - tan |- + --||
\ \2 12//
--------------------
2/a pi\
1 + tan |- + --|
\2 12/
$$\frac{2 \cdot \left(- \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1\right)}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1}$$
/ 1 \
2*|1 - ------------|
| 2/a pi\|
| cot |- + --||
\ \2 12//
--------------------
1
1 + ------------
2/a pi\
cot |- + --|
\2 12/
$$\frac{2 \cdot \left(1 - \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}\right)}{1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
2*|< |
|| / pi\ |
||cos|a + --| otherwise |
\\ \ 6 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\cos{\left(a + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases}\right)$$
// / 2*pi\ \
|| 0 for |a + ----| mod pi = 0|
|| \ 3 / |
2*|< |
|| / pi\ |
||cos|a + --| otherwise |
\\ \ 6 / /
$$2 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{2 \pi}{3}\right) \bmod \pi = 0 \\\cos{\left(a + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
2*|< |
|| / 2*pi\ |
||sin|a + ----| otherwise |
\\ \ 3 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\sin{\left(a + \frac{2 \pi}{3} \right)} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
2*|< 1 |
||----------- otherwise |
|| / pi\ |
||sec|a + --| |
\\ \ 6 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{1}{\sec{\left(a + \frac{\pi}{6} \right)}} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
2*|< 1 |
||------------ otherwise |
|| / pi\ |
||csc|-a + --| |
\\ \ 3 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{1}{\csc{\left(- a + \frac{\pi}{3} \right)}} & \text{otherwise} \end{cases}\right)$$
// / 2*pi\ \
|| 0 for |a + ----| mod pi = 0|
|| \ 3 / |
|| |
|| /a pi\ |
2*|< 2*cot|- + --| |
|| \2 3 / |
||---------------- otherwise |
|| 2/a pi\ |
||1 + cot |- + --| |
\\ \2 3 / /
$$2 \left(\begin{cases} 0 & \text{for}\: \left(a + \frac{2 \pi}{3}\right) \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} + \frac{\pi}{3} \right)}}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{3} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
/ 4/a pi\\
| 4*sin |- + --||
| \2 12/|
2*|1 - --------------|
| 2/ pi\ |
| sin |a + --| |
\ \ 6 / /
----------------------
4/a pi\
4*sin |- + --|
\2 12/
1 + --------------
2/ pi\
sin |a + --|
\ 6 /
$$\frac{2 \left(- \frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(a + \frac{\pi}{6} \right)}} + 1\right)}{\frac{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sin^{2}{\left(a + \frac{\pi}{6} \right)}} + 1}$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/a pi\ |
2*|<-1 + cot |- + --| |
|| \2 12/ |
||----------------- otherwise |
|| 2/a pi\ |
|| 1 + cot |- + --| |
\\ \2 12/ /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
/ 2/a pi\\
| 2*sin |- + --||
| \2 12/|
2*|1 - ---------------|
| / pi\|
| 1 + cos|a + --||
\ \ 6 //
-----------------------
2/a pi\
2*sin |- + --|
\2 12/
1 + ---------------
/ pi\
1 + cos|a + --|
\ 6 /
$$\frac{2 \cdot \left(- \frac{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos{\left(a + \frac{\pi}{6} \right)} + 1} + 1\right)}{\frac{2 \sin^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos{\left(a + \frac{\pi}{6} \right)} + 1} + 1}$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/a pi\ |
2*|<1 - tan |- + --| |
|| \2 12/ |
||---------------- otherwise |
|| 2/a pi\ |
||1 + tan |- + --| |
\\ \2 12/ /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{- \tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases}\right)$$
/ 2/a 5*pi\\
| cos |- - ----||
| \2 12 /|
2*|1 - --------------|
| 2/a pi\ |
| cos |- + --| |
\ \2 12/ /
----------------------
2/a 5*pi\
cos |- - ----|
\2 12 /
1 + --------------
2/a pi\
cos |- + --|
\2 12/
$$\frac{2 \left(- \frac{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1\right)}{\frac{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1}$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 1 |
||-1 + ------------ |
|| 2/a pi\ |
2*|< tan |- + --| |
|| \2 12/ |
||----------------- otherwise |
|| 1 |
|| 1 + ------------ |
|| 2/a pi\ |
|| tan |- + --| |
\\ \2 12/ /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}{1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
/ 2/ a 5*pi\\
| csc |- - + ----||
| \ 2 12 /|
2*|1 - ----------------|
| 2/a pi\ |
| csc |- + --| |
\ \2 12/ /
------------------------
2/ a 5*pi\
csc |- - + ----|
\ 2 12 /
1 + ----------------
2/a pi\
csc |- + --|
\2 12/
$$\frac{2 \left(- \frac{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1\right)}{\frac{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1}$$
/ 2/a pi\ \
| sec |- + --| |
| \2 12/ |
2*|1 - --------------|
| 2/a 5*pi\|
| sec |- - ----||
\ \2 12 //
----------------------
2/a pi\
sec |- + --|
\2 12/
1 + --------------
2/a 5*pi\
sec |- - ----|
\2 12 /
$$\frac{2 \cdot \left(1 - \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}\right)}{1 + \frac{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}}$$
/ 2 \
2*|1 - ------------------------------|
| / / pi\\ 2/a pi\|
| |1 + cos|a + --||*csc |- + --||
\ \ \ 6 // \2 12//
--------------------------------------
2
1 + ------------------------------
/ / pi\\ 2/a pi\
|1 + cos|a + --||*csc |- + --|
\ \ 6 // \2 12/
$$\frac{2 \cdot \left(1 - \frac{2}{\left(\cos{\left(a + \frac{\pi}{6} \right)} + 1\right) \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}\right)}{1 + \frac{2}{\left(\cos{\left(a + \frac{\pi}{6} \right)} + 1\right) \csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
||/ / pi\ |
2*|<| 1 for |a + --| mod 2*pi = 0 |
||| \ 6 / |
||< otherwise |
||| / pi\ |
|||cos|a + --| otherwise |
\\\ \ 6 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\cos{\left(a + \frac{\pi}{6} \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/ pi\ |
|| sin |a + --| |
|| \ 6 / |
||-1 + -------------- |
|| 4/a pi\ |
2*|< 4*sin |- + --| |
|| \2 12/ |
||------------------- otherwise |
|| 2/ pi\ |
|| sin |a + --| |
|| \ 6 / |
|| 1 + -------------- |
|| 4/a pi\ |
|| 4*sin |- + --| |
\\ \2 12/ /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\sin^{2}{\left(a + \frac{\pi}{6} \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}}{1 + \frac{\sin^{2}{\left(a + \frac{\pi}{6} \right)}}{4 \sin^{4}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/a pi\ |
|| 2*cos |- + --| |
|| \2 12/ |
||-1 + --------------- |
|| / pi\ |
2*|< 1 - cos|a + --| |
|| \ 6 / |
||-------------------- otherwise |
|| 2/a pi\ |
|| 2*cos |- + --| |
|| \2 12/ |
||1 + --------------- |
|| / pi\ |
|| 1 - cos|a + --| |
\\ \ 6 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\frac{2 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{- \cos{\left(a + \frac{\pi}{6} \right)} + 1} - 1}{\frac{2 \cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{- \cos{\left(a + \frac{\pi}{6} \right)} + 1} + 1} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
||/ / pi\ |
||| 1 for |a + --| mod 2*pi = 0 |
||| \ 6 / |
2*|<| |
||| 2/a pi\ |
||<-1 + cot |- + --| otherwise |
||| \2 12/ |
|||----------------- otherwise |
||| 2/a pi\ |
||| 1 + cot |- + --| |
\\\ \2 12/ /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} - 1}{\cot^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/a 5*pi\ |
|| sec |- - ----| |
|| \2 12 / |
||-1 + -------------- |
|| 2/a pi\ |
2*|< sec |- + --| |
|| \2 12/ |
||------------------- otherwise |
|| 2/a 5*pi\ |
|| sec |- - ----| |
|| \2 12 / |
|| 1 + -------------- |
|| 2/a pi\ |
|| sec |- + --| |
\\ \2 12/ /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{\frac{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} - 1}{\frac{\sec^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}{\sec^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}} + 1} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/a pi\ |
|| cos |- + --| |
|| \2 12/ |
||-1 + -------------- |
|| 2/a 5*pi\ |
2*|< cos |- - ----| |
|| \2 12 / |
||------------------- otherwise |
|| 2/a pi\ |
|| cos |- + --| |
|| \2 12/ |
|| 1 + -------------- |
|| 2/a 5*pi\ |
|| cos |- - ----| |
\\ \2 12 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}}{1 + \frac{\cos^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\cos^{2}{\left(\frac{a}{2} - \frac{5 \pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
// / pi\ \
|| 1 for |a + --| mod 2*pi = 0|
|| \ 6 / |
|| |
|| 2/a pi\ |
|| csc |- + --| |
|| \2 12/ |
||-1 + ---------------- |
|| 2/ a 5*pi\ |
2*|< csc |- - + ----| |
|| \ 2 12 / |
||--------------------- otherwise |
|| 2/a pi\ |
|| csc |- + --| |
|| \2 12/ |
|| 1 + ---------------- |
|| 2/ a 5*pi\ |
|| csc |- - + ----| |
\\ \ 2 12 / /
$$2 \left(\begin{cases} 1 & \text{for}\: \left(a + \frac{\pi}{6}\right) \bmod 2 \pi = 0 \\\frac{-1 + \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}}{1 + \frac{\csc^{2}{\left(\frac{a}{2} + \frac{\pi}{12} \right)}}{\csc^{2}{\left(- \frac{a}{2} + \frac{5 \pi}{12} \right)}}} & \text{otherwise} \end{cases}\right)$$
2*Piecewise((1, Mod(a + pi/6 = 2*pi, 0)), ((-1 + csc(a/2 + pi/12)^2/csc(-a/2 + 5*pi/12)^2)/(1 + csc(a/2 + pi/12)^2/csc(-a/2 + 5*pi/12)^2), True))