Тригонометрическая часть
[src]/ 0 for And(im(a) = 0, a mod pi = 0)
|
| 1
<------- otherwise
| 2
|csc (a)
\
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{1}{\csc^{2}{\left(a \right)}} & \text{otherwise} \end{cases}$$
1
------------
2/ pi\
sec |a - --|
\ 2 /
$$\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
|/ 0 for And(im(a) = 0, a mod pi = 0)
||
|| 2/a\
|| 4*cot |-|
<| \2/
|<-------------- otherwise otherwise
|| 2
||/ 2/a\\
|||1 + cot |-||
||\ \2//
\\
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
$$\sin^{2}{\left(a \right)}$$
2
1 1 - tan (a)
- - ---------------
2 / 2 \
2*\1 + tan (a)/
$$- \frac{1 - \tan^{2}{\left(a \right)}}{2 \left(\tan^{2}{\left(a \right)} + 1\right)} + \frac{1}{2}$$
1 1
- - ----------
2 2*sec(2*a)
$$\frac{1}{2} - \frac{1}{2 \sec{\left(2 a \right)}}$$
1 cos(2*a)
- - --------
2 2
$$\frac{1}{2} - \frac{\cos{\left(2 a \right)}}{2}$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
| 1
<------------ otherwise
| 2/ pi\
|sec |a - --|
\ \ 2 /
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{1}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}$$
$$\frac{1}{\csc^{2}{\left(a \right)}}$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
< 2
|sin (a) otherwise
\
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases}$$
2/a\
4*tan |-|
\2/
--------------
2
/ 2/a\\
|1 + tan |-||
\ \2//
$$\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}}$$
/pi \
sin|-- + 2*a|
1 \2 /
- - -------------
2 2
$$\frac{1}{2} - \frac{\sin{\left(2 a + \frac{\pi}{2} \right)}}{2}$$
/ 1 for And(im(a) = 0, a mod pi = 0)
|
| 2
<-1 + cot (a)
|------------ otherwise
| 2
1 \1 + cot (a)
- - -----------------------------------------------
2 2
$$\frac{1}{2} - \left(\frac{\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} & \text{otherwise} \end{cases}}{2}\right)$$
/ 1 for And(im(a) = 0, a mod pi = 0)
<
1 \cos(2*a) otherwise
- - -------------------------------------------
2 2
$$\frac{1}{2} - \left(\frac{\begin{cases} 1 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\cos{\left(2 a \right)} & \text{otherwise} \end{cases}}{2}\right)$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
< 2/ pi\
|cos |a - --| otherwise
\ \ 2 /
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\cos^{2}{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
| 2/a\
| 4*cot |-|
| \2/
<-------------- otherwise
| 2
|/ 2/a\\
||1 + cot |-||
|\ \2//
\
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{4 \cot^{2}{\left(\frac{a}{2} \right)}}{\left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}$$
1 1
- - ---------------
2 /pi \
2*csc|-- - 2*a|
\2 /
$$\frac{1}{2} - \frac{1}{2 \csc{\left(- 2 a + \frac{\pi}{2} \right)}}$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
| 2/a\
| 4*tan |-|
| \2/
<-------------- otherwise
| 2
|/ 2/a\\
||1 + tan |-||
|\ \2//
\
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{4 \tan^{2}{\left(\frac{a}{2} \right)}}{\left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2}} & \text{otherwise} \end{cases}$$
2/ pi\
cos |a - --|
\ 2 /
$$\cos^{2}{\left(a - \frac{\pi}{2} \right)}$$
/ 0 for And(im(a) = 0, a mod pi = 0)
|
|/ 0 for And(im(a) = 0, a mod pi = 0)
<|
|< 2 otherwise
||sin (a) otherwise
\\
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\sin^{2}{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$