sin(a-pi)еслиa=3/2 (упростите выражение)

Вы ввели

sin(a - pi)

$$\sin{\left(a - \pi \right)}$$

Подстановка условия

sin(a - pi) при a = 3/2

подставляем

sin(a - pi)

$$\sin{\left(a - \pi \right)}$$

-sin(a)

$$- \sin{\left(a \right)}$$

переменные

a = 3/2

$$a = \frac{3}{2}$$

-sin((3/2))

$$- \sin{\left((3/2) \right)}$$

-sin(3/2)

$$- \sin{\left(\frac{3}{2} \right)}$$

Степени

   /   I*(pi - a)    I*(a - pi)\ 
-I*\- e           + e          / 
---------------------------------
                2                

$$- \frac{i \left(- e^{i \left(\pi - a\right)} + e^{i \left(a - \pi\right)}\right)}{2}$$

-sin(a)

$$- \sin{\left(a \right)}$$

Численный ответ

sin(a - pi)

Рациональный знаменатель

-sin(a)

$$- \sin{\left(a \right)}$$

Объединение рациональных выражений

-sin(a)

$$- \sin{\left(a \right)}$$

Общее упрощение

-sin(a)

$$- \sin{\left(a \right)}$$

Собрать выражение

-sin(a)

$$- \sin{\left (a \right )}$$

Тригонометрическая часть

/                     0                        for And(im(a) = 0, a mod pi = 0)
|                                                                              
< //  0     for And(im(a) = 0, a mod pi = 0)\                                  
|-|<                                        |             otherwise            
\ \\sin(a)             otherwise            /                                  

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$

    /    pi\
-cos|a - --|
    \    2 /

$$- \cos{\left(a - \frac{\pi}{2} \right)}$$

/     0       for And(im(a) = 0, a mod pi = 0)
|                                             
|       /a\                                   
| -2*tan|-|                                   
<       \2/                                   
|-----------             otherwise            
|       2/a\                                  
|1 + tan |-|                                  
\        \2/                                  

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}$$

/     0        for And(im(a) = 0, a mod pi = 0)
|                                              
<    /    pi\                                  
|-cos|a - --|             otherwise            
\    \    2 /                                  

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \cos{\left(a - \frac{\pi}{2} \right)} & \text{otherwise} \end{cases}$$

       /a\ 
 -2*cot|-| 
       \2/ 
-----------
       2/a\
1 + cot |-|
        \2/

$$- \frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1}$$

/     0       for And(im(a) = 0, a mod pi = 0)
|                                             
|    -1                                       
<-----------             otherwise            
|   /    pi\                                  
|sec|a - --|                                  
\   \    2 /                                  

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}} & \text{otherwise} \end{cases}$$

/         0            for And(im(a) = 0, a mod pi = 0)
|                                                      
|        -2                                            
|--------------------             otherwise            

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \frac{2}{\left(1 + \frac{1}{\cot^{2}{\left(\frac{a}{2} \right)}}\right) \cot{\left(\frac{a}{2} \right)}} & \text{otherwise} \end{cases}$$

      1      
-------------
   /    3*pi\
sec|a - ----|
   \     2  /

$$\frac{1}{\sec{\left(a - \frac{3 \pi}{2} \right)}}$$

 //  0     for And(im(a) = 0, a mod pi = 0)\
-|<                                        |
 \\sin(a)             otherwise            /

$$- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\sin{\left(a \right)} & \text{otherwise} \end{cases}$$

-sin(a)

$$- \sin{\left(a \right)}$$

       /a\ 
 -2*tan|-| 
       \2/ 
-----------
       2/a\
1 + tan |-|
        \2/

$$- \frac{2 \tan{\left(\frac{a}{2} \right)}}{\tan^{2}{\left(\frac{a}{2} \right)} + 1}$$

    -1     
-----------
   /    pi\
sec|a - --|
   \    2 /

$$- \frac{1}{\sec{\left(a - \frac{\pi}{2} \right)}}$$

 //     0       for And(im(a) = 0, a mod pi = 0)\
 ||                                             |
 ||       /a\                                   |
 ||  2*cot|-|                                   |
-|<       \2/                                   |
 ||-----------             otherwise            |
 ||       2/a\                                  |
 ||1 + cot |-|                                  |
 \\        \2/                                  /

$$- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases}$$

   /    3*pi\
cos|a - ----|
   \     2  /

$$\cos{\left(a - \frac{3 \pi}{2} \right)}$$

        -2          
--------------------
/       1   \    /a\
|1 + -------|*tan|-|
|       2/a\|    \2/
|    tan |-||       
\        \2//       

$$- \frac{2}{\left(1 + \frac{1}{\tan^{2}{\left(\frac{a}{2} \right)}}\right) \tan{\left(\frac{a}{2} \right)}}$$

 -1   
------
csc(a)

$$- \frac{1}{\csc{\left(a \right)}}$$

/                        0                          for And(im(a) = 0, a mod pi = 0)
|                                                                                   
| //     0       for And(im(a) = 0, a mod pi = 0)\                                  
| ||                                             |                                  
| ||       /a\                                   |                                  
< ||  2*cot|-|                                   |                                  
|-|<       \2/                                   |             otherwise            
| ||-----------             otherwise            |                                  
| ||       2/a\                                  |                                  
| ||1 + cot |-|                                  |                                  
\ \\        \2/                                  /                                  

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\\frac{2 \cot{\left(\frac{a}{2} \right)}}{\cot^{2}{\left(\frac{a}{2} \right)} + 1} & \text{otherwise} \end{cases} & \text{otherwise} \end{cases}$$

/  0     for And(im(a) = 0, a mod pi = 0)
|                                        
< -1                                     
|------             otherwise            
\csc(a)                                  

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \frac{1}{\csc{\left(a \right)}} & \text{otherwise} \end{cases}$$

/   0     for And(im(a) = 0, a mod pi = 0)
<                                         
\-sin(a)             otherwise            

$$\begin{cases} 0 & \text{for}\: \operatorname{im}{\left(a\right)} = 0 \wedge a \bmod \pi = 0 \\- \sin{\left(a \right)} & \text{otherwise} \end{cases}$$

Комбинаторика

-sin(a)

$$- \sin{\left(a \right)}$$

Раскрыть выражение

-sin(a)

$$- \sin{\left(a \right)}$$