Господин Экзамен
asinh(sin(x)) если x=3
Решение
Вы ввели
[src]
asinh(sin(x))
$$\operatorname{asinh}{\left(\sin{\left(x \right)} \right)}$$
asinh(sin(x))
Подстановка условия
[src]
asinh(sin(x)) при x = 3
подставляем
asinh(sin(x))
$$\operatorname{asinh}{\left(\sin{\left(x \right)} \right)}$$
asinh(sin(x))
$$\operatorname{asinh}{\left(\sin{\left(x \right)} \right)}$$
переменные
x = 3
$$x = 3$$
asinh(sin((3)))
$$\operatorname{asinh}{\left(\sin{\left((3) \right)} \right)}$$
asinh(sin(3))
$$\operatorname{asinh}{\left(\sin{\left(3 \right)} \right)}$$
asinh(sin(3))
Степени
[src]
/ / -I*x I*x\\
|I*\- e + e /|
-asinh|------------------|
\ 2 /
$$- \operatorname{asinh}{\left(\frac{i \left(e^{i x} - e^{- i x}\right)}{2} \right)}$$
-asinh(i*(-exp(-i*x) + exp(i*x))/2)
Тригонометрическая часть
[src]
/ 1 \
asinh|------|
\csc(x)/
$$\operatorname{asinh}{\left(\frac{1}{\csc{\left(x \right)}} \right)}$$
/ / pi\\
asinh|cos|x - --||
\ \ 2 //
$$\operatorname{asinh}{\left(\cos{\left(x - \frac{\pi}{2} \right)} \right)}$$
/ 1 \
asinh|-----------|
\csc(pi - x)/
$$\operatorname{asinh}{\left(\frac{1}{\csc{\left(- x + \pi \right)}} \right)}$$
/ 1 \
asinh|-----------|
| / pi\|
|sec|x - --||
\ \ 2 //
$$\operatorname{asinh}{\left(\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} \right)}$$
/ 1 \
asinh|-----------|
| /pi \|
|sec|-- - x||
\ \2 //
$$\operatorname{asinh}{\left(\frac{1}{\sec{\left(- x + \frac{\pi}{2} \right)}} \right)}$$
/ /x\\
asinh|(1 + cos(x))*tan|-||
\ \2//
$$\operatorname{asinh}{\left(\left(\cos{\left(x \right)} + 1\right) \tan{\left(\frac{x}{2} \right)} \right)}$$
/ /x\ \
| 2*cot|-| |
| \2/ |
asinh|-----------|
| 2/x\|
|1 + cot |-||
\ \2//
$$\operatorname{asinh}{\left(\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} \right)}$$
/ /x\ \
| 2*tan|-| |
| \2/ |
asinh|-----------|
| 2/x\|
|1 + tan |-||
\ \2//
$$\operatorname{asinh}{\left(\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} \right)}$$
// 0 for x mod pi = 0\
asinh|< |
\\sin(x) otherwise /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases} \right)}$$
/ 2 \
asinh|--------------------|
|/ 1 \ /x\|
||1 + -------|*cot|-||
|| 2/x\| \2/|
|| cot |-|| |
\\ \2// /
$$\operatorname{asinh}{\left(\frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right) \cot{\left(\frac{x}{2} \right)}} \right)}$$
// 0 for x mod pi = 0\
|| |
asinh|< 1 |
||------ otherwise |
\\csc(x) /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\csc{\left(x \right)}} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
asinh|< / pi\ |
||cos|x - --| otherwise |
\\ \ 2 / /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\cos{\left(x - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases} \right)}$$
// 2/x pi\\ \
||1 - cot |- + --||*(1 + sin(x))|
|\ \2 4 // |
asinh|-------------------------------|
\ 2 /
$$\operatorname{asinh}{\left(\frac{\left(- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1\right) \left(\sin{\left(x \right)} + 1\right)}{2} \right)}$$
/ 2/x pi\\
|-1 + tan |- + --||
| \2 4 /|
asinh|-----------------|
| 2/x pi\|
| 1 + tan |- + --||
\ \2 4 //
$$\operatorname{asinh}{\left(\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} \right)}$$
/ 2/x pi\\
|1 - cot |- + --||
| \2 4 /|
asinh|----------------|
| 2/x pi\|
|1 + cot |- + --||
\ \2 4 //
$$\operatorname{asinh}{\left(\frac{- \cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1}{\cot^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} \right)}$$
// 0 for x mod pi = 0\
|| |
|| 1 |
asinh|<----------- otherwise |
|| / pi\ |
||sec|x - --| |
\\ \ 2 / /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{1}{\sec{\left(x - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
/ 2/x\ \
| 4*sin |-|*sin(x) |
| \2/ |
asinh|-------------------|
| 2 4/x\|
|sin (x) + 4*sin |-||
\ \2//
$$\operatorname{asinh}{\left(\frac{4 \sin^{2}{\left(\frac{x}{2} \right)} \sin{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)} + \sin^{2}{\left(x \right)}} \right)}$$
// / 3*pi\ \
|| 1 for |x + ----| mod 2*pi = 0|
asinh|< \ 2 / |
|| |
\\sin(x) otherwise /
$$\operatorname{asinh}{\left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
||1 - cos(x) |
asinh|<---------- otherwise |
|| /x\ |
|| tan|-| |
\\ \2/ /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{- \cos{\left(x \right)} + 1}{\tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
/ 2/x\ \
| 4*sin |-| |
| \2/ |
asinh|----------------------|
|/ 4/x\\ |
|| 4*sin |-|| |
|| \2/| |
||1 + ---------|*sin(x)|
|| 2 | |
\\ sin (x) / /
$$\operatorname{asinh}{\left(\frac{4 \sin^{2}{\left(\frac{x}{2} \right)}}{\left(\frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right) \sin{\left(x \right)}} \right)}$$
// 0 for x mod pi = 0\
|| |
|| /x\ |
|| 2*tan|-| |
asinh|< \2/ |
||----------- otherwise |
|| 2/x\ |
||1 + tan |-| |
\\ \2/ /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \tan{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| /x\ |
|| 2*cot|-| |
asinh|< \2/ |
||----------- otherwise |
|| 2/x\ |
||1 + cot |-| |
\\ \2/ /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
asinh|
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\sin{\left(x \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| 2 |
||-------------------- otherwise |
asinh|
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right) \tan{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
/ /x\ \
| 2*sec|-| |
| \2/ |
asinh|------------------------------|
|/ 2/x\ \ |
|| sec |-| | |
|| \2/ | /x pi\|
||1 + ------------|*sec|- - --||
|| 2/x pi\| \2 2 /|
|| sec |- - --|| |
\\ \2 2 // /
$$\operatorname{asinh}{\left(\frac{2 \sec{\left(\frac{x}{2} \right)}}{\left(\frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} \right)}$$
/ /x pi\ \
| 2*cos|- - --| |
| \2 2 / |
asinh|-------------------------|
|/ 2/x pi\\ |
|| cos |- - --|| |
|| \2 2 /| /x\|
||1 + ------------|*cos|-||
|| 2/x\ | \2/|
|| cos |-| | |
\\ \2/ / /
$$\operatorname{asinh}{\left(\frac{2 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right) \cos{\left(\frac{x}{2} \right)}} \right)}$$
/ /pi x\ \
| 2*csc|-- - -| |
| \2 2/ |
asinh|-------------------------|
|/ 2/pi x\\ |
|| csc |-- - -|| |
|| \2 2/| /x\|
||1 + ------------|*csc|-||
|| 2/x\ | \2/|
|| csc |-| | |
\\ \2/ / /
$$\operatorname{asinh}{\left(\frac{2 \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right) \csc{\left(\frac{x}{2} \right)}} \right)}$$
// / 3*pi\ \
|| 1 for |x + ----| mod 2*pi = 0|
|| \ 2 / |
|| |
|| 2/x pi\ |
asinh|<-1 + tan |- + --| |
|| \2 4 / |
||----------------- otherwise |
|| 2/x pi\ |
|| 1 + tan |- + --| |
\\ \2 4 / /
$$\operatorname{asinh}{\left(\begin{cases} 1 & \text{for}\: \left(x + \frac{3 \pi}{2}\right) \bmod 2 \pi = 0 \\\frac{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} - 1}{\tan^{2}{\left(\frac{x}{2} + \frac{\pi}{4} \right)} + 1} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| sin(x) |
||----------------------- otherwise |
||/ 2 \ |
asinh|<| sin (x) | 2/x\ |
|||1 + ---------|*sin |-| |
||| 4/x\| \2/ |
||| 4*sin |-|| |
||\ \2// |
\\ /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{\sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \sin^{2}{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
||/ 0 for x mod pi = 0 |
||| |
||| /x\ |
asinh|<| 2*cot|-| |
||< \2/ otherwise |
|||----------- otherwise |
||| 2/x\ |
|||1 + cot |-| |
\\\ \2/ /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{x}{2} \right)}}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| 2*sin(x) |
||---------------------------- otherwise |
|| / 2 \ |
asinh|< | sin (x) | |
||(1 - cos(x))*|1 + ---------| |
|| | 4/x\| |
|| | 4*sin |-|| |
|| \ \2// |
\\ /
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sin{\left(x \right)}}{\left(1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right) \left(- \cos{\left(x \right)} + 1\right)} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| /x pi\ |
|| 2*sec|- - --| |
|| \2 2 / |
||------------------------- otherwise |
asinh|
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\left(1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right) \sec{\left(\frac{x}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| /x\ |
|| 2*cos|-| |
|| \2/ |
||------------------------------ otherwise |
asinh|
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \cos{\left(\frac{x}{2} \right)}}{\left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
// 0 for x mod pi = 0\
|| |
|| /x\ |
|| 2*csc|-| |
|| \2/ |
||------------------------------ otherwise |
asinh|
$$\operatorname{asinh}{\left(\begin{cases} 0 & \text{for}\: x \bmod \pi = 0 \\\frac{2 \csc{\left(\frac{x}{2} \right)}}{\left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases} \right)}$$
asinh(Piecewise((0, Mod(x = pi, 0)), (2*csc(x/2)/((1 + csc(x/2)^2/csc(pi/2 - x/2)^2)*csc(pi/2 - x/2)), True)))