Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 2*x^2-x-1=x^2-5*x-(-1-x^2)
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Equation 9*(x-5)=-x
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Equation cos(x)=3
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Equation 2-3*(2*x+2)=5-4*x
- Express {x} in terms of y where:
- -11*x-14*y=-3
- 10*x-2*y=0
- 10*x+1*y=10
- 2*x+2*y=-6
- Derivative of:
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cos(x)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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Identical expressions
- cos(x)= three
- co sinus of e of (x) equally 3
- co sinus of e of (x) equally three
- cosx=3
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Similar expressions
- (cos(2*x)*cos(8*x)-cos(10*x))/cos(x+1)=0
- cosx+2sin(pi+x)-sin(pi/2-x)=-1
- cosx=3
cos(x)=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = 3$$
- this is the simplest trigonometric equation
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.
$$\cos{\left(x \right)} = 3$$
- 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.
Sum and product of roots
[src]
sum
2*pi - I*im(acos(3)) + I*im(acos(3)) + re(acos(3))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right)$$
=
2*pi + re(acos(3))
$$\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + 2 \pi$$
product
(2*pi - I*im(acos(3)))*(I*im(acos(3)) + re(acos(3)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right)$$
=
(2*pi - I*im(acos(3)))*(I*im(acos(3)) + re(acos(3)))
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}\right)$$
(2*pi - i*im(acos(3)))*(i*im(acos(3)) + re(acos(3)))
Rapid solution
[src]
x1 = 2*pi - I*im(acos(3))
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}$$
x2 = I*im(acos(3)) + re(acos(3))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(3 \right)}\right)}$$
x2 = re(acos(3)) + i*im(acos(3))
Numerical answer
[src]
x1 = 6.28318530717959 - 1.76274717403909*i
x2 = 1.76274717403909*i
x2 = 1.76274717403909*i
The graph