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sin((pi(x-3))/4)=sqrt(2) equation

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Numerical solution:

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The solution

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   /pi*(x - 3)\     ___
sin|----------| = \/ 2 
   \    4     /        
$$\sin{\left(\frac{\pi \left(x - 3\right)}{4} \right)} = \sqrt{2}$$
Detail solution
Given the equation
$$\sin{\left(\frac{\pi \left(x - 3\right)}{4} \right)} = \sqrt{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by -1

The equation is transformed to
$$\sin{\left(\frac{\pi x}{4} + \frac{\pi}{4} \right)} = - \sqrt{2}$$
As right part of the equation
modulo =
True

but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
The graph
Rapid solution [src]
                /    /  ___\\         /    /  ___\\
       pi + 4*re\asin\\/ 2 //   4*I*im\asin\\/ 2 //
x1 = - ---------------------- - -------------------
                 pi                      pi        
$$x_{1} = - \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} - \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}$$
             /    /  ___\\         /    /  ___\\
         4*re\asin\\/ 2 //   4*I*im\asin\\/ 2 //
x2 = 3 + ----------------- + -------------------
                 pi                   pi        
$$x_{2} = \frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3 + \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}$$
x2 = 4*re(asin(sqrt(2)))/pi + 3 + 4*i*im(asin(sqrt(2)))/pi
Sum and product of roots [src]
sum
           /    /  ___\\         /    /  ___\\           /    /  ___\\         /    /  ___\\
  pi + 4*re\asin\\/ 2 //   4*I*im\asin\\/ 2 //       4*re\asin\\/ 2 //   4*I*im\asin\\/ 2 //
- ---------------------- - ------------------- + 3 + ----------------- + -------------------
            pi                      pi                       pi                   pi        
$$\left(\frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3 + \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right) + \left(- \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} - \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right)$$
=
             /    /  ___\\       /    /  ___\\
    pi + 4*re\asin\\/ 2 //   4*re\asin\\/ 2 //
3 - ---------------------- + -----------------
              pi                     pi       
$$- \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + \frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3$$
product
/           /    /  ___\\         /    /  ___\\\ /        /    /  ___\\         /    /  ___\\\
|  pi + 4*re\asin\\/ 2 //   4*I*im\asin\\/ 2 //| |    4*re\asin\\/ 2 //   4*I*im\asin\\/ 2 //|
|- ---------------------- - -------------------|*|3 + ----------------- + -------------------|
\            pi                      pi        / \            pi                   pi        /
$$\left(- \frac{\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} - \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right) \left(\frac{4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi} + 3 + \frac{4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}}{\pi}\right)$$
=
 /         /    /  ___\\         /    /  ___\\\ /           /    /  ___\\         /    /  ___\\\ 
-\pi + 4*re\asin\\/ 2 // + 4*I*im\asin\\/ 2 ///*\3*pi + 4*re\asin\\/ 2 // + 4*I*im\asin\\/ 2 /// 
-------------------------------------------------------------------------------------------------
                                                 2                                               
                                               pi                                                
$$- \frac{\left(\pi + 4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + 4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right) \left(4 \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + 3 \pi + 4 i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right)}{\pi^{2}}$$
-(pi + 4*re(asin(sqrt(2))) + 4*i*im(asin(sqrt(2))))*(3*pi + 4*re(asin(sqrt(2))) + 4*i*im(asin(sqrt(2))))/pi^2
Numerical answer [src]
x1 = -3.0 + 1.12219970467836*i
x2 = 5.0 - 1.12219970467836*i
x2 = 5.0 - 1.12219970467836*i