Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 3*x^2-12*x+12=0
-
Equation 4*x^2-11*x-3=0
-
Equation 10x+1=6x
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Equation sin(z)=3
- Express {x} in terms of y where:
- 4*x+5*y=7
- 12*x+14*y=9
- -13*x+10*y=-18
- 12*x+10*y=14
- Limit of the function:
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sin(z)
- Integral of d{x}:
- sin(z)
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Identical expressions
- sin(z)= three
- sinus of (z) equally 3
- sinus of (z) equally three
- sinz=3
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Similar expressions
- sin2z+5(sinz+cosz)+1=0
- sinz=-2
sin(z)=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(z \right)} = 3$$
- 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.
$$\sin{\left(z \right)} = 3$$
- 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.
Rapid solution
[src]
z1 = pi - re(asin(3)) - I*im(asin(3))
$$z_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
z2 = I*im(asin(3)) + re(asin(3))
$$z_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
z2 = re(asin(3)) + i*im(asin(3))
Sum and product of roots
[src]
sum
pi - re(asin(3)) - I*im(asin(3)) + I*im(asin(3)) + re(asin(3))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(3)) - I*im(asin(3)))*(I*im(asin(3)) + re(asin(3)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
-(I*im(asin(3)) + re(asin(3)))*(-pi + I*im(asin(3)) + re(asin(3)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
-(i*im(asin(3)) + re(asin(3)))*(-pi + i*im(asin(3)) + re(asin(3)))
Numerical answer
[src]
z1 = 1.5707963267949 + 1.76274717403909*i
z2 = 1.5707963267949 - 1.76274717403909*i
z2 = 1.5707963267949 - 1.76274717403909*i
The graph