Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin(x)=2
-
Equation x^4=(4*x-21)^2
-
Equation sin(x^2)=0
-
Equation (x+2)^2+(x-3)^2=2x^2
- Express {x} in terms of y where:
- -19*x-14*y=-8
- 9*x+8*y=6
- 4*x+15*y=19
- 4*x+16*y=6
- Derivative of:
-
sin(x)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)= two
- sinus of (x) equally 2
- sinus of (x) equally two
- sinx=2
-
Similar expressions
- sin(x^2)=0
- cosx+sinx=sqrt2*sin(2x)
- 5*sin^2x+21*sinx+4=0
- sinx=0,8634
- 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