Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x^2-8*x+17=0
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Equation 2-3(7+2x)=11
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Equation x^2-2x+1=0
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Equation 7+8x=-2x-5
- Express {x} in terms of y where:
- 7*x+19*y=12
- 17*x+20*y=-12
- 18*x-11*y=2
- 2*x-8*y=4
- Derivative of:
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0,5
- Sum of series:
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0,5
- Integral of d{x}:
- 0,5
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Identical expressions
- sin*(pi*x)/ three = zero , five
- sinus of multiply by ( Pi multiply by x) divide by 3 equally 0,5
- sinus of multiply by ( Pi multiply by x) divide by three equally zero , five
- sin(pix)/3=0,5
- sinpix/3=0,5
- sin*(pi*x)/3=O,5
- sin*(pi*x) divide by 3=0,5
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Similar expressions
- sin(pi*x)/3=1
- sin(pi*x)/3=-1/2
- sin(pi*x/3)=1/2
sin*(pi*x)/3=0,5 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
sin(pi*x)
--------- = 1/2
3
$$\frac{\sin{\left(\pi x \right)}}{3} = \frac{1}{2}$$
Detail solution
Given the equation
$$\frac{\sin{\left(\pi x \right)}}{3} = \frac{1}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\pi x \right)} = \frac{3}{2}$$
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.
$$\frac{\sin{\left(\pi x \right)}}{3} = \frac{1}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/3
The equation is transformed to
$$\sin{\left(\pi x \right)} = \frac{3}{2}$$
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.
Rapid solution
[src]
pi - re(asin(3/2)) I*im(asin(3/2))
x1 = ------------------ - ---------------
pi pi
$$x_{1} = \frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}$$
re(asin(3/2)) I*im(asin(3/2))
x2 = ------------- + ---------------
pi pi
$$x_{2} = \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}$$
Sum and product of roots
[src]
sum
pi - re(asin(3/2)) I*im(asin(3/2)) re(asin(3/2)) I*im(asin(3/2))
0 + ------------------ - --------------- + ------------- + ---------------
pi pi pi pi
$$\left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right) + \left(0 + \left(\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right)\right)$$
=
pi - re(asin(3/2)) re(asin(3/2))
------------------ + -------------
pi pi
$$\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} + \frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}$$
product
/pi - re(asin(3/2)) I*im(asin(3/2))\ /re(asin(3/2)) I*im(asin(3/2))\ 1*|------------------ - ---------------|*|------------- + ---------------| \ pi pi / \ pi pi /
$$1 \left(\frac{\pi - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} - \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right) \left(\frac{\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi} + \frac{i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}}{\pi}\right)$$
=
(I*im(asin(3/2)) + re(asin(3/2)))*(pi - re(asin(3/2)) - I*im(asin(3/2)))
------------------------------------------------------------------------
2
pi
$$\frac{\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)}{\pi^{2}}$$
(i*im(asin(3/2)) + re(asin(3/2)))*(pi - re(asin(3/2)) - i*im(asin(3/2)))/pi^2
Numerical answer
[src]
x1 = 0.5 + 0.306348962530033*i
x2 = 0.5 - 0.306348962530033*i
x2 = 0.5 - 0.306348962530033*i
The graph