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sin(x)=3

sin(x)=3 equation

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Numerical solution:

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The solution

You have entered [src] 
sin(x) = 3
sin⁡(x)=3\sin{\left(x \right)} = 3
Simplify
Detail solution
Given the equation
sin⁡(x)=3\sin{\left(x \right)} = 3
- 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(3)) - I*im(asin(3))
x1=−re⁡(asin⁡(3))+π−iim⁡(asin⁡(3))x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}
Simplify 
x2 = I*im(asin(3)) + re(asin(3))
x2=re⁡(asin⁡(3))+iim⁡(asin⁡(3))x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}
Simplify
Sum and product of roots [src] 
sum
0 + pi - re(asin(3)) - I*im(asin(3)) + I*im(asin(3)) + re(asin(3))
(re⁡(asin⁡(3))+iim⁡(asin⁡(3)))−(−π+re⁡(asin⁡(3))+iim⁡(asin⁡(3)))\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) - \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) 
=
pi
π\pi 
product
1*(pi - re(asin(3)) - I*im(asin(3)))*(I*im(asin(3)) + re(asin(3)))
(re⁡(asin⁡(3))+iim⁡(asin⁡(3)))1(−re⁡(asin⁡(3))+π−iim⁡(asin⁡(3)))\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) 
=
-(I*im(asin(3)) + re(asin(3)))*(-pi + I*im(asin(3)) + re(asin(3)))
−(re⁡(asin⁡(3))+iim⁡(asin⁡(3)))(−π+re⁡(asin⁡(3))+iim⁡(asin⁡(3)))- \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) 
-(i*im(asin(3)) + re(asin(3)))*(-pi + i*im(asin(3)) + re(asin(3)))
Numerical answer [src] 
x1 = 1.5707963267949 + 1.76274717403909*i
x2 = 1.5707963267949 - 1.76274717403909*i
x2 = 1.5707963267949 - 1.76274717403909*i
The graph
sin(x)=3 equation
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