Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x*8=25+15
-
Equation cos(x)=5
- Equation (x-4)^4-4*(x-4)^2-21=0
-
Equation ((1/5))^(x)^(2)*5^(2*x+2)=(1/5)^(6)
- Express {x} in terms of y where:
- 15*x-5*y=-5
- 15*x+7*y=2
- 12*x-20*y=10
- -11*x-1*y=15
- Derivative of:
-
cos(x)/5
- Graphing y =:
-
cos(x)/5
-
Identical expressions
- cos(x)/ five = one
- co sinus of e of (x) divide by 5 equally 1
- co sinus of e of (x) divide by five equally one
- cosx/5=1
- cos(x) divide by 5=1
-
Similar expressions
- cos(x/5)=-(\sqrt(3))/(2)
- 2cos(x/5)=5
- cosx/5=1/2
- sqrt(cos(x)^2-cos(x))/5-1=0
- cosx/5=1
cos(x)/5=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{5} = 1$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(x \right)} = 5$$
As right part of the equation
modulo =
but cos
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\frac{\cos{\left(x \right)}}{5} = 1$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/5
The equation is transformed to
$$\cos{\left(x \right)} = 5$$
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.
Rapid solution
[src]
x1 = 2*pi - I*im(acos(5))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}$$
x2 = I*im(acos(5)) + re(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))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)$$
=
2*pi + re(acos(5))
$$\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + 2 \pi$$
product
(2*pi - I*im(acos(5)))*(I*im(acos(5)) + re(acos(5)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)$$
=
(2*pi - I*im(acos(5)))*(I*im(acos(5)) + re(acos(5)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(5 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(5 \right)}\right)}\right)$$
(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