sin(4*pi+x)еслиx=-1 (упростите выражение)

Вы ввели

sin(4*pi + x)

$$\sin{\left(x + 4 \pi \right)}$$

Подстановка условия

sin(4*pi + x) при x = -1

подставляем

sin(4*pi + x)

$$\sin{\left(x + 4 \pi \right)}$$

sin(x)

$$\sin{\left(x \right)}$$

переменные

x = -1

$$x = -1$$

sin((-1))

$$\sin{\left((-1) \right)}$$

sin(-1)

$$\sin{\left(-1 \right)}$$

-sin(1)

$$- \sin{\left(1 \right)}$$

Степени

sin(x)

$$\sin{\left(x \right)}$$

   /   I*(-x - 4*pi)    I*(x + 4*pi)\ 
-I*\- e              + e            / 
--------------------------------------
                  2                   

$$- \frac{i \left(- e^{i \left(- x - 4 \pi\right)} + e^{i \left(x + 4 \pi\right)}\right)}{2}$$

Численный ответ

sin(4*pi + x)

Рациональный знаменатель

sin(x)

$$\sin{\left(x \right)}$$

Объединение рациональных выражений

sin(x)

$$\sin{\left(x \right)}$$

Общее упрощение

sin(x)

$$\sin{\left(x \right)}$$

Собрать выражение

sin(x)

$$\sin{\left (x \right )}$$

Общий знаменатель

sin(x)

$$\sin{\left(x \right)}$$

Тригонометрическая часть

       /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)
|                                                                           

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

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

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

  1   
------
csc(x)

$$\frac{1}{\csc{\left(x \right)}}$$

/     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(x)

$$\sin{\left(x \right)}$$

   /    pi\
cos|x - --|
   \    2 /

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

/     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)                                  

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

Комбинаторика

sin(x)

$$\sin{\left(x \right)}$$

Раскрыть выражение

sin(x)

$$\sin{\left(x \right)}$$