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\sin(\pi(4x+12))/(6)=(1)/(2) equation

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Numerical solution:

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The solution

You have entered [src]
sin(pi*(4*x + 12))      
------------------ = 0.5
        6               
$$\frac{\sin{\left(\pi \left(4 x + 12\right) \right)}}{6} = 0.5$$
Detail solution
Given the equation
$$\frac{\sin{\left(\pi \left(4 x + 12\right) \right)}}{6} = 0.5$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/6

The equation is transformed to
$$\sin{\left(4 \pi x \right)} = 3$$
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
Sum and product of roots [src]
sum
0.125 - 0.140274963084795*I + 0.125 + 0.140274963084795*I
$$\left(0.125 - 0.140274963084795 i\right) + \left(0.125 + 0.140274963084795 i\right)$$
=
0.250000000000000
$$0.25$$
product
(0.125 - 0.140274963084795*I)*(0.125 + 0.140274963084795*I)
$$\left(0.125 - 0.140274963084795 i\right) \left(0.125 + 0.140274963084795 i\right)$$
=
0.0353020652684406
$$0.0353020652684406$$
0.0353020652684406
Rapid solution [src]
x1 = 0.125 - 0.140274963084795*I
$$x_{1} = 0.125 - 0.140274963084795 i$$
x2 = 0.125 + 0.140274963084795*I
$$x_{2} = 0.125 + 0.140274963084795 i$$
x2 = 0.125 + 0.140274963084795*i
Numerical answer [src]
x1 = 0.125 - 0.140274963084795*i
x2 = 0.125 + 0.140274963084795*i
x2 = 0.125 + 0.140274963084795*i