Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2+3x+2=0
- Equation x+y=5
-
Equation sin(x)=3
-
Equation x^2-11*x+30=0
- Express {x} in terms of y where:
- 6*x+17*y=-11
- -13*x+7*y=-15
- -14*x-8*y=20
- 9*x+14*y=-10
- Derivative of:
-
sin(x)
- Integral of d{x}:
-
sin(x)
- Canonical form:
- sin(x)
-
Identical expressions
- sin(x)= three
- sinus of (x) equally 3
- sinus of (x) equally three
- sinx=3
-
Similar expressions
- sin3x-sin7x+cos4x+sinx=(1)/(2)
- sinx=3
sin(x)=3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = 3$$
- 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.
$$\sin{\left(x \right)} = 3$$
- 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]
x1 = pi - re(asin(3)) - I*im(asin(3))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
x2 = I*im(asin(3)) + re(asin(3))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
Sum and product of roots
[src]
sum
0 + pi - re(asin(3)) - I*im(asin(3)) + I*im(asin(3)) + re(asin(3))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) - \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
1*(pi - re(asin(3)) - I*im(asin(3)))*(I*im(asin(3)) + re(asin(3)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) 1 \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
-(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]
x1 = 1.5707963267949 + 1.76274717403909*i
x2 = 1.5707963267949 - 1.76274717403909*i
x2 = 1.5707963267949 - 1.76274717403909*i
The graph