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sin(x)=2

sin(x)=2 equation

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Numerical solution:

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The solution

You have entered [src] 
sin(x) = 2
sin⁡(x)=2\sin{\left(x \right)} = 2
Simplify
Detail solution
Given the equation
sin⁡(x)=2\sin{\left(x \right)} = 2
- this is the simplest trigonometric equation
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
0-80-60-40-2020406080-1001005-5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
x1 = pi - re(asin(2)) - I*im(asin(2))
x1=−re⁡(asin⁡(2))+π−iim⁡(asin⁡(2))x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)} 
x2 = I*im(asin(2)) + re(asin(2))
x2=re⁡(asin⁡(2))+iim⁡(asin⁡(2))x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)} 
x2 = re(asin(2)) + i*im(asin(2))
Sum and product of roots [src] 
sum
pi - re(asin(2)) - I*im(asin(2)) + I*im(asin(2)) + re(asin(2))
(re⁡(asin⁡(2))+iim⁡(asin⁡(2)))+(−re⁡(asin⁡(2))+π−iim⁡(asin⁡(2)))\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) 
=
pi
π\pi 
product
(pi - re(asin(2)) - I*im(asin(2)))*(I*im(asin(2)) + re(asin(2)))
(re⁡(asin⁡(2))+iim⁡(asin⁡(2)))(−re⁡(asin⁡(2))+π−iim⁡(asin⁡(2)))\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) 
=
-(I*im(asin(2)) + re(asin(2)))*(-pi + I*im(asin(2)) + re(asin(2)))
−(re⁡(asin⁡(2))+iim⁡(asin⁡(2)))(−π+re⁡(asin⁡(2))+iim⁡(asin⁡(2)))- \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) 
-(i*im(asin(2)) + re(asin(2)))*(-pi + i*im(asin(2)) + re(asin(2)))
Numerical answer [src] 
x1 = 1.5707963267949 + 1.31695789692482*i
x2 = 1.5707963267949 - 1.31695789692482*i
x2 = 1.5707963267949 - 1.31695789692482*i
The graph
sin(x)=2 equation
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