Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -24-y=-16
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Equation 4(x-6)=x-9
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Equation x*(x^2+8*x+16)=5*(x+4)
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Equation -x^2+4x+3=x^2-x-(1+2x^2)
- Express {x} in terms of y where:
- 10*x-15*y=16
- -18*x-6*y=-1
- -6*x-10*y=19
- -1*x-17*y=-12
- Integral of d{x}:
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sinx/2
- Derivative of:
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sinx/2
- Graphing y =:
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sinx/2
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Identical expressions
- sinx/ two =-√ two
- sinus of x divide by 2 equally minus √2
- sinus of x divide by two equally minus √ two
- sinx divide by 2=-√2
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Similar expressions
- sin(x)*cos(x)+sqrt(3)*sin(x)/2=0
- pi*x/360-sin(x)/2=0,2*pi
- sin(x/2)=-1/2
- sinx/2=+√2
sinx/2=-√2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\sin{\left(x \right)}}{2} = - \sqrt{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = - 2 \sqrt{2}$$
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.
$$\frac{\sin{\left(x \right)}}{2} = - \sqrt{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/2
The equation is transformed to
$$\sin{\left(x \right)} = - 2 \sqrt{2}$$
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.
Sum and product of roots
[src]
sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\ pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 // + - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ \pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\- re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 ///
$$\left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ -\I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)$$
-(i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))*(pi + i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))
Rapid solution
[src]
/ / ___\\ / / ___\\ x1 = pi + I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 //
$$x_{1} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}$$
/ / ___\\ / / ___\\ x2 = - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 //
$$x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}$$
x2 = -re(asin(2*sqrt(2))) - i*im(asin(2*sqrt(2)))
Numerical answer
[src]
x1 = 4.71238898038469 - 1.70004220705667*i
x2 = -1.5707963267949 + 1.70004220705667*i
x2 = -1.5707963267949 + 1.70004220705667*i