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cos(x)=5

cos(x)=5 equation

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Numerical solution:

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The solution

You have entered [src] 
cos(x) = 5
cos⁡(x)=5\cos{\left(x \right)} = 5
Simplify
Detail solution
Given the equation
cos⁡(x)=5\cos{\left(x \right)} = 5
- 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
0-80-60-40-2020406080-100100-510
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
0 + 2*pi - I*im(acos(5)) + I*im(acos(5)) + re(acos(5))
(0+(2π−iim⁡(acos⁡(5))))+(re⁡(acos⁡(5))+iim⁡(acos⁡(5)))\left(0 + \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) 
=
2*pi + re(acos(5))
re⁡(acos⁡(5))+2π\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + 2 \pi 
product
1*(2*pi - I*im(acos(5)))*(I*im(acos(5)) + re(acos(5)))
1⋅(2π−iim⁡(acos⁡(5)))(re⁡(acos⁡(5))+iim⁡(acos⁡(5)))1 \cdot \left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) 
=
(2*pi - I*im(acos(5)))*(I*im(acos(5)) + re(acos(5)))
(2π−iim⁡(acos⁡(5)))(re⁡(acos⁡(5))+iim⁡(acos⁡(5)))\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) 
(2*pi - i*im(acos(5)))*(i*im(acos(5)) + re(acos(5)))
Rapid solution [src] 
x1 = 2*pi - I*im(acos(5))
x1=2π−iim⁡(acos⁡(5))x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}
Simplify 
x2 = I*im(acos(5)) + re(acos(5))
x2=re⁡(acos⁡(5))+iim⁡(acos⁡(5))x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}
Simplify
Numerical answer [src] 
x1 = 6.28318530717959 - 2.29243166956118*i
x2 = 2.29243166956118*i
x2 = 2.29243166956118*i
The graph
cos(x)=5 equation
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