2cos(x/5)=5 equation

The teacher will be very surprised to see your correct solution 😉

You have entered [src]

     /x\    
2*cos|-| = 5
     \5/

2 \cos{\left(\frac{x}{5} \right)} = 5

Simplify

Detail solution

Given the equation

2 \cos{\left(\frac{x}{5} \right)} = 5

- this is the simplest trigonometric equation

Divide both parts of the equation by 2

The equation is transformed to

\cos{\left(\frac{x}{5} \right)} = \frac{5}{2}

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

Plot the graph f1(x)

Plot the graph f2(x)

Sum and product of roots [src]

sum

10*pi - 5*I*im(acos(5/2)) + 5*I*im(acos(5/2))

\left(10 \pi - 5 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right) + 5 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}

10*pi

10 \pi

product

(10*pi - 5*I*im(acos(5/2)))*5*I*im(acos(5/2))

5 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} \left(10 \pi - 5 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}\right)

25*(2*pi*I + im(acos(5/2)))*im(acos(5/2))

25 \left(\operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)} + 2 i \pi\right) \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}

25*(2*pi*i + im(acos(5/2)))*im(acos(5/2))

Rapid solution [src]

x1 = 10*pi - 5*I*im(acos(5/2))

x_{1} = 10 \pi - 5 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}

x2 = 5*I*im(acos(5/2))

x_{2} = 5 i \operatorname{im}{\left(\operatorname{acos}{\left(\frac{5}{2} \right)}\right)}

x2 = 5*i*im(acos(5/2))

Numerical answer [src]

x1 = 31.4159265358979 - 7.83399618486206*i

x2 = 7.83399618486206*i

x2 = 7.83399618486206*i