Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation tan(x)=0
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Equation sin(x)=2
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Equation 1-2*(5-2*x)=-x-3
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Equation (7x+1)-(9x+3)=5
- Express {x} in terms of y where:
- (x^2+y^2-1)^3-x^2*y^3=0
- -19*x-14*y=-8
- -2*x+1*y=-8
- -2*x-1*y=-8
- Derivative of:
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sin(x)
- Integral of d{x}:
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sin(x)
- Canonical form:
- sin(x)
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Identical expressions
- sin(x)= two
- sinus of (x) equally 2
- sinus of (x) equally two
- sinx=2
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Similar expressions
- cosx+sinx=sqrt2*sin(2x)
- x^2+x+lg(sinx)=1+lg(sinx)
- sqrt2*sin(pi/4-x/2)+sin(x/2)=sqrt3/2
- sinx=2
sin(x)=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = 2$$
- 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.
$$\sin{\left(x \right)} = 2$$
- 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]
x1 = pi - re(asin(2)) - I*im(asin(2))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}$$
x2 = I*im(asin(2)) + re(asin(2))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}$$
x2 = re(asin(2)) + i*im(asin(2))
Sum and product of roots
[src]
sum
pi - re(asin(2)) - I*im(asin(2)) + I*im(asin(2)) + re(asin(2))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(2)) - I*im(asin(2)))*(I*im(asin(2)) + re(asin(2)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)$$
=
-(I*im(asin(2)) + re(asin(2)))*(-pi + I*im(asin(2)) + re(asin(2)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(2 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(2 \right)}\right)}\right)$$
-(i*im(asin(2)) + re(asin(2)))*(-pi + i*im(asin(2)) + re(asin(2)))
Numerical answer
[src]
x1 = 1.5707963267949 + 1.31695789692482*i
x2 = 1.5707963267949 - 1.31695789692482*i
x2 = 1.5707963267949 - 1.31695789692482*i
The graph