Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation (x+2)/9=(x-3)/2
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Equation (x-2)^4+3*(x-2)^2-10=0
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Equation 3*x^2-18=0
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Equation (x-3)*(x+2)=0
- Express {x} in terms of y where:
- 2*x+3*y=14
- 18*x-8*y=-2
- 16*x-7*y=-5
- 10*x-16*y=-6
- Sum of series:
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√3
- Integral of d{x}:
- √3
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Identical expressions
- two sin*x/2=√ three
- 2 sinus of multiply by x divide by 2 equally √3
- two sinus of multiply by x divide by 2 equally √ three
- 2sinx/2=√3
- 2sin*x divide by 2=√3
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Similar expressions
- 2*sin(x/2)=-sqrt(3)
- 2sinx/2=√2
- Sqrt(2(sin(x/2*(1-cos(x)))^2))=-sin(-x)-5cos(x)
- 2*sin(x/2-pi/6)=1
- sin(x/2)*cos(3x/2)-1/√(3)*sin(2x)=sin(3x/2)*cos(x/2)
2sin*x/2=√3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2*sin(x) ___ -------- = \/ 3 2
$$\frac{2 \sin{\left(x \right)}}{2} = \sqrt{3}$$
Detail solution
Given the equation
$$\frac{2 \sin{\left(x \right)}}{2} = \sqrt{3}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
$$\frac{2 \sin{\left(x \right)}}{2} = \sqrt{3}$$
- this is the simplest trigonometric equation
As right part of the equation
modulo =
True
but sin
can no be more than 1 or less than -1
so the solution of the equation d'not exist.
Rapid solution
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/ / ___\\ / / ___\\ x1 = pi - re\asin\\/ 3 // - I*im\asin\\/ 3 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}$$
/ / ___\\ / / ___\\ x2 = I*im\asin\\/ 3 // + re\asin\\/ 3 //
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}$$
x2 = re(asin(sqrt(3))) + i*im(asin(sqrt(3)))
Sum and product of roots
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sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ pi - re\asin\\/ 3 // - I*im\asin\\/ 3 // + I*im\asin\\/ 3 // + re\asin\\/ 3 //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ \pi - re\asin\\/ 3 // - I*im\asin\\/ 3 ///*\I*im\asin\\/ 3 // + re\asin\\/ 3 ///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ -\I*im\asin\\/ 3 // + re\asin\\/ 3 ///*\-pi + I*im\asin\\/ 3 // + re\asin\\/ 3 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{3} \right)}\right)}\right)$$
-(i*im(asin(sqrt(3))) + re(asin(sqrt(3))))*(-pi + i*im(asin(sqrt(3))) + re(asin(sqrt(3))))
Numerical answer
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x1 = 1.5707963267949 + 1.14621583478059*i
x2 = 1.5707963267949 - 1.14621583478059*i
x2 = 1.5707963267949 - 1.14621583478059*i