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sin(6*x)=9/8

sin(6*x)=9/8 equation

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Numerical solution:

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The solution

You have entered [src] 
sin(6*x) = 9/8
sin⁡(6x)=98\sin{\left(6 x \right)} = \frac{9}{8}
Simplify
Detail solution
Given the equation
sin⁡(6x)=98\sin{\left(6 x \right)} = \frac{9}{8}
- 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
0-80-60-40-2020406080-1001002.5-2.5
Plot the graph f1(x)
Plot the graph f2(x)
Rapid solution [src] 
       re(asin(9/8))   pi   I*im(asin(9/8))
x1 = - ------------- + -- - ---------------
             6         6           6
x1=−re⁡(asin⁡(98))6+π6−iim⁡(asin⁡(98))6x_{1} = - \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{\pi}{6} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}
Simplify 
     re(asin(9/8))   I*im(asin(9/8))
x2 = ------------- + ---------------
           6                6
x2=re⁡(asin⁡(98))6+iim⁡(asin⁡(98))6x_{2} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}
Simplify
Sum and product of roots [src] 
sum
      re(asin(9/8))   pi   I*im(asin(9/8))   re(asin(9/8))   I*im(asin(9/8))
0 + - ------------- + -- - --------------- + ------------- + ---------------
            6         6           6                6                6
(re⁡(asin⁡(98))6+iim⁡(asin⁡(98))6)−(−π6+re⁡(asin⁡(98))6+iim⁡(asin⁡(98))6)\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right) - \left(- \frac{\pi}{6} + \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right) 
=
pi
--
6
π6\frac{\pi}{6} 
product
  /  re(asin(9/8))   pi   I*im(asin(9/8))\ /re(asin(9/8))   I*im(asin(9/8))\
1*|- ------------- + -- - ---------------|*|------------- + ---------------|
  \        6         6           6       / \      6                6       /
(re⁡(asin⁡(98))6+iim⁡(asin⁡(98))6)1(−re⁡(asin⁡(98))6+π6−iim⁡(asin⁡(98))6)\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right) 1 \left(- \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6} + \frac{\pi}{6} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}}{6}\right) 
=
-(I*im(asin(9/8)) + re(asin(9/8)))*(-pi + I*im(asin(9/8)) + re(asin(9/8))) 
---------------------------------------------------------------------------
                                     36
−(re⁡(asin⁡(98))+iim⁡(asin⁡(98)))(−π+re⁡(asin⁡(98))+iim⁡(asin⁡(98)))36- \frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{9}{8} \right)}\right)}\right)}{36} 
-(i*im(asin(9/8)) + re(asin(9/8)))*(-pi + i*im(asin(9/8)) + re(asin(9/8)))/36
Numerical answer [src] 
x1 = 0.261799387799149 + 0.0824888205157545*i
x2 = 0.261799387799149 - 0.0824888205157545*i
x2 = 0.261799387799149 - 0.0824888205157545*i
The graph
sin(6*x)=9/8 equation
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