Mister Exam

Other calculators

cos(x)/5=1

cos(x)/5=1 equation

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

v

Numerical solution:

Do search numerical solution at [, ]

The solution

You have entered [src] 
cos(x)    
------ = 1
  5
cos⁡(x)5=1\frac{\cos{\left(x \right)}}{5} = 1
Simplify
Detail solution
Given the equation
cos⁡(x)5=1\frac{\cos{\left(x \right)}}{5} = 1
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/5

The equation is transformed to
cos⁡(x)=5\cos{\left(x \right)} = 5
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
0-80-60-40-2020406080-1001002-1
Plot the graph f1(x)
Plot the graph f2(x)
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)} 
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)} 
x2 = re(acos(5)) + i*im(acos(5))
Sum and product of roots [src] 
sum
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 + re(acos(5))
re⁡(acos⁡(5))+2π\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + 2 \pi 
product
(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)))
(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)))
Numerical answer [src] 
x1 = 6.28318530717959 - 2.29243166956118*i
x2 = 2.29243166956118*i
x2 = 2.29243166956118*i
The graph
cos(x)/5=1 equation
    © Mister Exam – Calculator