Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation cos(x)=-3
-
Equation (x+3)^3=81*(x+3)
-
Equation x^4=(3x-10)^2
-
Equation 4^x+3=11^x
- Express {x} in terms of y where:
- -20*x+5*y=13
- 9*x+9*y=18
- -11*x-16*y=-19
- 3*x-3*y=-14
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Identical expressions
- cosx/ two + one = zero
- co sinus of e of x divide by 2 plus 1 equally 0
- co sinus of e of x divide by two plus one equally zero
- cosx/2+1=O
- cosx divide by 2+1=0
-
Similar expressions
- cosx/2-1=0
- -17cos(x)/2+17/2=0
cosx/2+1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\cos{\left(x \right)}}{2} + 1 = 0$$
- this is the simplest trigonometric equation
We get:
$$\frac{\cos{\left(x \right)}}{2} = -1$$
The equation is transformed to
$$\cos{\left(x \right)} = -2$$
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.
$$\frac{\cos{\left(x \right)}}{2} + 1 = 0$$
- this is the simplest trigonometric equation
Move 1 to right part of the equation
with the change of sign in 1
We get:
$$\frac{\cos{\left(x \right)}}{2} = -1$$
Divide both parts of the equation by 1/2
The equation is transformed to
$$\cos{\left(x \right)} = -2$$
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
-re(acos(-2)) + 2*pi - I*im(acos(-2)) + I*im(acos(-2)) + re(acos(-2))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right)$$
=
2*pi
$$2 \pi$$
product
(-re(acos(-2)) + 2*pi - I*im(acos(-2)))*(I*im(acos(-2)) + re(acos(-2)))
$$\left(\operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}\right)$$
=
-(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)))
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))
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(-2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(-2 \right)}\right)}$$
x2 = re(acos(-2)) + i*im(acos(-2))
Numerical answer
[src]
x1 = 3.14159265358979 + 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i
x2 = 3.14159265358979 - 1.31695789692482*i