Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x/12+x/8+x=-29/6
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Equation x^2+7x-18=0
- Equation x-y+2=0
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Equation x^2-2x=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
- Derivative of:
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cos(x)
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sqrt(3)
- Graphing y =:
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cos(x)
- Integral of d{x}:
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cos(x)
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sqrt(3)
- The double integral of:
- sqrt(3)
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Identical expressions
- cos(x)=sqrt(three)
- co sinus of e of (x) equally square root of (3)
- co sinus of e of (x) equally square root of (three)
- cos(x)=√(3)
- cosx=sqrt3
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Similar expressions
- sqrt(3*x+1)=x-1
- cos(x+(pi/6))=-1
- cosx=sqrt(3)
cos(x)=sqrt(3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\cos{\left(x \right)} = \sqrt{3}$$
- 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.
$$\cos{\left(x \right)} = \sqrt{3}$$
- 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 //
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}\right) + \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}\right)$$
=
/ / ___\\ 2*pi + re\acos\\/ 3 //
$$\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)} + 2 \pi$$
product
/ / / ___\\\ / / / ___\\ / / ___\\\ \2*pi - I*im\acos\\/ 3 ///*\I*im\acos\\/ 3 // + re\acos\\/ 3 ///
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}\right)$$
=
/ / / ___\\\ / / / ___\\ / / ___\\\ \2*pi - I*im\acos\\/ 3 ///*\I*im\acos\\/ 3 // + re\acos\\/ 3 ///
$$\left(2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}\right)$$
(2*pi - i*im(acos(sqrt(3))))*(i*im(acos(sqrt(3))) + re(acos(sqrt(3))))
Rapid solution
[src]
/ / ___\\ x1 = 2*pi - I*im\acos\\/ 3 //
$$x_{1} = 2 \pi - i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}$$
/ / ___\\ / / ___\\ x2 = I*im\acos\\/ 3 // + re\acos\\/ 3 //
$$x_{2} = \operatorname{re}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{acos}{\left(\sqrt{3} \right)}\right)}$$
x2 = re(acos(sqrt(3))) + i*im(acos(sqrt(3)))
Numerical answer
[src]
x1 = 6.28318530717959 - 1.14621583478059*i
x2 = 1.14621583478059*i
x2 = 1.14621583478059*i
The graph