Подстановка условия
[src]$$\sin{\left(x + 4 \pi \right)}$$
$$\sin{\left(x \right)}$$
$$\sin{\left((-1) \right)}$$
$$\sin{\left(-1 \right)}$$
$$- \sin{\left(1 \right)}$$
Тригонометрическая часть
[src] /x\
2*tan|-|
\2/
-----------
2/x\
1 + tan |-|
\2/
$$\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
| /x\
| 2*tan|-|
< \2/
|----------- otherwise
| 2/x\
|1 + tan |-|
\ \2/
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
| 1
<----------- otherwise
| / pi\
|sec|x - --|
\ \ 2 /
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
<
\sin(x) otherwise
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases}$$
/ 7*pi\
cos|x + ----|
\ 2 /
$$\cos{\left(x + \frac{7 \pi}{2} \right)}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
|/ 0 for And(im(x) = 0, x mod pi = 0)
||
|| /x\
<| 2*cot|-|
|< \2/ otherwise
||----------- otherwise
|| 2/x\
||1 + cot |-|
\\ \2/
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
0 for And(im(x) = 0, x mod pi = 0)
|< otherwise
\\sin(x) otherwise
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$
1
-----------
/ pi\
sec|x - --|
\ 2 /
$$\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}}$$
$$\frac{1}{\csc{\left(x \right)}}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
| /x\
| 2*cot|-|
< \2/
|----------- otherwise
| 2/x\
|1 + cot |-|
\ \2/
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases}$$
1
-------------
/ 7*pi\
sec|x + ----|
\ 2 /
$$\frac{1}{\sec{\left(x + \frac{7 \pi}{2} \right)}}$$
$$\sin{\left(x \right)}$$
$$\cos{\left(x - \frac{\pi}{2} \right)}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
< / pi\
|cos|x - --| otherwise
\ \ 2 /
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\cos{\left(x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}$$
/ 0 for And(im(x) = 0, x mod pi = 0)
|
< 1
|------ otherwise
\csc(x)
$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(x\right)} = 0 \wedge x \bmod \pi = 0 \\\frac{1}{\csc{\left(x \right)}} & \text{otherwise} \end{cases}$$