Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3-x/7=x/3
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Equation tan(x)=-2
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Equation sin(x)=pi/3
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Equation -2(x-4)=3+7x
- Express {x} in terms of y where:
- 2*x+2*y=-6
- 7*x+20*y=-17
- -11*x+15*y=7
- 14*x-13*y=-10
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
- pi/3
- Canonical form:
- sin(x)
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Identical expressions
- sin(x)=pi/ three
- sinus of (x) equally Pi divide by 3
- sinus of (x) equally Pi divide by three
- sinx=pi/3
- sin(x)=pi divide by 3
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Similar expressions
- sin(x-(1/2))-x+(1/2)=0
- sinx=pi/3
sin(x)=pi/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = \frac{\pi}{3}$$
- 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.
$$\sin{\left(x \right)} = \frac{\pi}{3}$$
- 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.
Sum and product of roots
[src]
sum
/ /pi\\ / /pi\\ / /pi\\ / /pi\\
pi - re|asin|--|| - I*im|asin|--|| + I*im|asin|--|| + re|asin|--||
\ \3 // \ \3 // \ \3 // \ \3 //
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
/ / /pi\\ / /pi\\\ / / /pi\\ / /pi\\\ |pi - re|asin|--|| - I*im|asin|--|||*|I*im|asin|--|| + re|asin|--||| \ \ \3 // \ \3 /// \ \ \3 // \ \3 ///
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right)$$
=
/ / /pi\\ / /pi\\\ / / /pi\\ / /pi\\\ -|I*im|asin|--|| + re|asin|--|||*|-pi + I*im|asin|--|| + re|asin|--||| \ \ \3 // \ \3 /// \ \ \3 // \ \3 ///
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}\right)$$
-(i*im(asin(pi/3)) + re(asin(pi/3)))*(-pi + i*im(asin(pi/3)) + re(asin(pi/3)))
Rapid solution
[src]
/ /pi\\ / /pi\\
x1 = pi - re|asin|--|| - I*im|asin|--||
\ \3 // \ \3 //
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}$$
/ /pi\\ / /pi\\
x2 = I*im|asin|--|| + re|asin|--||
\ \3 // \ \3 //
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{\pi}{3} \right)}\right)}$$
x2 = re(asin(pi/3)) + i*im(asin(pi/3))
Numerical answer
[src]
x1 = 1.5707963267949 + 0.306042108613266*i
x2 = 1.5707963267949 - 0.306042108613266*i
x2 = 1.5707963267949 - 0.306042108613266*i
The graph