Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2+9=(x+9)^2
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Equation 9x-7=6x+14
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Equation x+3=-9*x
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Equation 3-x/7=x/3
- Express {x} in terms of y where:
- 1*x-6*y=-19
- -1*x-20*y=-17
- -13*x+7*y=11
- -13*x-19*y=17
- Derivative of:
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cos(x)
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-2
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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-2
- Sum of series:
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-2
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Identical expressions
- cos(x)=- two
- co sinus of e of (x) equally minus 2
- co sinus of e of (x) equally minus two
- cosx=-2
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Similar expressions
- (sqrt2*sin^2x+cosx-sqrt2)*(sqrt6*sinx)=0
- cos(x)=+2
- cosx=-2
cos(x)=-2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = -2$$
- 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.
$$\cos{\left(x \right)} = -2$$
- 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.
Rapid solution
[src]
x1 = -re(acos(-2)) + 2*pi - I*im(acos(-2))
$$x_{1} = - \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}$$
x2 = I*im(acos(-2)) + re(acos(-2))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}$$
Sum and product of roots
[src]
sum
0 + -re(acos(-2)) + 2*pi - I*im(acos(-2)) + I*im(acos(-2)) + re(acos(-2))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) - \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
1*(-re(acos(-2)) + 2*pi - I*im(acos(-2)))*(I*im(acos(-2)) + re(acos(-2)))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right)$$
=
-(I*im(acos(-2)) + re(acos(-2)))*(-2*pi + I*im(acos(-2)) + re(acos(-2)))
$$- \left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) \left(- 2 \pi + \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right)$$
-(i*im(acos(-2)) + re(acos(-2)))*(-2*pi + i*im(acos(-2)) + re(acos(-2)))
Numerical answer
[src]
x1 = 3.14159265358979 + 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i
The graph