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cos(x)=3

cos(x)=3 equation

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Numerical solution:

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The solution

You have entered [src] 
cos(x) = 3
cos⁡(x)=3\cos{\left(x \right)} = 3
Simplify
Detail solution
Given the equation
cos⁡(x)=3\cos{\left(x \right)} = 3
- this is the simplest trigonometric equation
As right part of the equation
modulo =
True

but cos
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)
Sum and product of roots [src] 
sum
2*pi - I*im(acos(3)) + I*im(acos(3)) + re(acos(3))
(2π−iim⁡(acos⁡(3)))+(re⁡(acos⁡(3))+iim⁡(acos⁡(3)))\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) 
=
2*pi + re(acos(3))
re⁡(acos⁡(3))+2π\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + 2 \pi 
product
(2*pi - I*im(acos(3)))*(I*im(acos(3)) + re(acos(3)))
(2π−iim⁡(acos⁡(3)))(re⁡(acos⁡(3))+iim⁡(acos⁡(3)))\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) 
=
(2*pi - I*im(acos(3)))*(I*im(acos(3)) + re(acos(3)))
(2π−iim⁡(acos⁡(3)))(re⁡(acos⁡(3))+iim⁡(acos⁡(3)))\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) 
(2*pi - i*im(acos(3)))*(i*im(acos(3)) + re(acos(3)))
Rapid solution [src] 
x1 = 2*pi - I*im(acos(3))
x1=2π−iim⁡(acos⁡(3))x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)} 
x2 = I*im(acos(3)) + re(acos(3))
x2=re⁡(acos⁡(3))+iim⁡(acos⁡(3))x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)} 
x2 = re(acos(3)) + i*im(acos(3))
Numerical answer [src] 
x1 = 6.28318530717959 - 1.76274717403909*i
x2 = 1.76274717403909*i
x2 = 1.76274717403909*i
The graph
cos(x)=3 equation
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