Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3/(x-5)+8/x=2
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Equation 0,144:(3,4-x)=2,4
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Equation (-2x+1)*(-2x-7)=0
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Equation 1/x^2-1/x-6=0
- Express {x} in terms of y where:
- -5*x-2*y=9
- 8*x-19*y=16
- 3*x-12*y=3
- 19*x+6*y=8
- Limit of the function:
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sqrt(2)/2
- sqrt(2)/2
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Identical expressions
- sin(pi*x)/ four =sqrt(two)/ two
- sinus of ( Pi multiply by x) divide by 4 equally square root of (2) divide by 2
- sinus of ( Pi multiply by x) divide by four equally square root of (two) divide by two
- sin(pi*x)/4=√(2)/2
- sin(pix)/4=sqrt(2)/2
- sinpix/4=sqrt2/2
- sin(pi*x) divide by 4=sqrt(2) divide by 2
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Similar expressions
- x^2-4*x+5=sin(pi*x/4)
- sin((pi*x)/4)=1
- sin((pi*x)/4)=0.5
- sin(pi*x/4)+1=cos(pi*x/8)+sqrt(2)*cos(pi*x/8-pi/4)
sin(pi*x)/4=sqrt(2)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
sin(pi*x) \/ 2
--------- = -----
4 2
$$\frac{\sin{\left(\pi x \right)}}{4} = \frac{\sqrt{2}}{2}$$
Detail solution
Given the equation
$$\frac{\sin{\left(\pi x \right)}}{4} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\pi x \right)} = 2 \sqrt{2}$$
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.
$$\frac{\sin{\left(\pi x \right)}}{4} = \frac{\sqrt{2}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/4
The equation is transformed to
$$\sin{\left(\pi x \right)} = 2 \sqrt{2}$$
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
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sum
/ / ___\\ / / ___\\ / / ___\\ / / ___\\
pi - re\asin\2*\/ 2 // I*im\asin\2*\/ 2 // re\asin\2*\/ 2 // I*im\asin\2*\/ 2 //
---------------------- - ------------------- + ----------------- + -------------------
pi pi pi pi
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}\right) + \left(\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}\right)$$
=
/ / ___\\ / / ___\\
pi - re\asin\2*\/ 2 // re\asin\2*\/ 2 //
---------------------- + -----------------
pi pi
$$\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} + \frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}$$
product
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\ |pi - re\asin\2*\/ 2 // I*im\asin\2*\/ 2 //| |re\asin\2*\/ 2 // I*im\asin\2*\/ 2 //| |---------------------- - -------------------|*|----------------- + -------------------| \ pi pi / \ pi pi /
$$\left(\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}\right) \left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}\right)$$
=
/ / / ___\\ / / ___\\\ / / / ___\\ / / ___\\\
\I*im\asin\2*\/ 2 // + re\asin\2*\/ 2 ///*\pi - re\asin\2*\/ 2 // - I*im\asin\2*\/ 2 ///
----------------------------------------------------------------------------------------
2
pi
$$\frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}\right)}{\pi^{2}}$$
(i*im(asin(2*sqrt(2))) + re(asin(2*sqrt(2))))*(pi - re(asin(2*sqrt(2))) - i*im(asin(2*sqrt(2))))/pi^2
Rapid solution
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/ / ___\\ / / ___\\
pi - re\asin\2*\/ 2 // I*im\asin\2*\/ 2 //
x1 = ---------------------- - -------------------
pi pi
$$x_{1} = \frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}$$
/ / ___\\ / / ___\\
re\asin\2*\/ 2 // I*im\asin\2*\/ 2 //
x2 = ----------------- + -------------------
pi pi
$$x_{2} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(2 \sqrt{2} \right)}\right)}}{\pi}$$
x2 = re(asin(2*sqrt(2)))/pi + i*im(asin(2*sqrt(2)))/pi
Numerical answer
[src]
x1 = 0.5 + 0.541140241435849*i
x2 = 0.5 - 0.541140241435849*i
x2 = 0.5 - 0.541140241435849*i