Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x-11)*(-x+9)=0
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Equation 2^x=5
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Equation (x-10)^2=(x+4)^2
-
Equation 2*sin(x)+1=0
- Express {x} in terms of y where:
- 7*x+6*y=20
- -7*x-19*y=-18
- -12*x-8*y=13
- 15*x-5*y=-5
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Identical expressions
- 2cos(x/ five)= five
- 2 co sinus of e of (x divide by 5) equally 5
- 2 co sinus of e of (x divide by five) equally five
- 2cosx/5=5
- 2cos(x divide by 5)=5
-
Similar expressions
- 2*cos(x/5)+cos(2*x/5)-2*cos(4*x/5)-cos(7*x/5)-cos(x)+cos(2*x)=0
2cos(x/5)=5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \cos{\left(\frac{x}{5} \right)} = 5$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\cos{\left(\frac{x}{5} \right)} = \frac{5}{2}$$
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.
$$2 \cos{\left(\frac{x}{5} \right)} = 5$$
- 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.
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