Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 4-6*(x+2)=3-5*x
-
Equation -x-4+5(x+3)=5(-1-x)-2
-
Equation 49,86-(0.3+0.049*49,86)=x
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Equation x^2-5x+4=0
- Express {x} in terms of y where:
- -11*x+15*y=7
- 6*x+17*y=3
- 4*x+2*y=5
- 1*x+10*y=-18
- Derivative of:
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√2
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Identical expressions
- two sinx/ two =√2
- 2 sinus of x divide by 2 equally √2
- two sinus of x divide by two equally √2
- 2sinx divide by 2=√2
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Similar expressions
- 2*sin(x/2-pi/6)=1
- 2*sin(x/2)=-sqrt(3)
- Sqrt(2(sin(x/2*(1-cos(x)))^2))=-sin(-x)-5cos(x)
- 2sin*x/2=sqrt3
2sinx/2=√2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
2*sin(x) ___ -------- = \/ 2 2
$$\frac{2 \sin{\left(x \right)}}{2} = \sqrt{2}$$
Detail solution
Given the equation
$$\frac{2 \sin{\left(x \right)}}{2} = \sqrt{2}$$
- 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.
$$\frac{2 \sin{\left(x \right)}}{2} = \sqrt{2}$$
- 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\\/ 2 // - I*im\asin\\/ 2 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}$$
/ / ___\\ / / ___\\ x2 = I*im\asin\\/ 2 // + re\asin\\/ 2 //
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}$$
x2 = re(asin(sqrt(2))) + i*im(asin(sqrt(2)))
Sum and product of roots
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sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ pi - re\asin\\/ 2 // - I*im\asin\\/ 2 // + I*im\asin\\/ 2 // + re\asin\\/ 2 //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ \pi - re\asin\\/ 2 // - I*im\asin\\/ 2 ///*\I*im\asin\\/ 2 // + re\asin\\/ 2 ///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ -\I*im\asin\\/ 2 // + re\asin\\/ 2 ///*\-pi + I*im\asin\\/ 2 // + re\asin\\/ 2 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\sqrt{2} \right)}\right)}\right)$$
-(i*im(asin(sqrt(2))) + re(asin(sqrt(2))))*(-pi + i*im(asin(sqrt(2))) + re(asin(sqrt(2))))
Numerical answer
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x1 = 1.5707963267949 + 0.881373587019543*i
x2 = 1.5707963267949 - 0.881373587019543*i
x2 = 1.5707963267949 - 0.881373587019543*i