Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation x+5=0
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Equation a+120=4000/5
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Equation 11/(x+4)=-11/7
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Equation sin(x)=-3
- Express {x} in terms of y where:
- 16*x+17*y=-13
- 7*x+14*y=-14
- -10*x-6*y=16
- 2*x+18*y=8
- Derivative of:
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sin(x)
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-3
- Integral of d{x}:
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sin(x)
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-3
- Canonical form:
- sin(x)
- Sum of series:
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-3
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Identical expressions
- sin(x)=- three
- sinus of (x) equally minus 3
- sinus of (x) equally minus three
- sinx=-3
-
Similar expressions
- sin(x)=+3
- 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.
Sum and product of roots
[src]
sum
pi + I*im(asin(3)) + re(asin(3)) + -re(asin(3)) - I*im(asin(3))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi + I*im(asin(3)) + re(asin(3)))*(-re(asin(3)) - I*im(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)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right) \left(\operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} + \pi + i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}\right)$$
-(i*im(asin(3)) + re(asin(3)))*(pi + i*im(asin(3)) + re(asin(3)))
Rapid solution
[src]
x1 = pi + I*im(asin(3)) + re(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 = -re(asin(3)) - I*im(asin(3))
$$x_{2} = - \operatorname{re}{\left(\operatorname{asin}{\left(3 \right)}\right)} - i \operatorname{im}{\left(\operatorname{asin}{\left(3 \right)}\right)}$$
x2 = -re(asin(3)) - i*im(asin(3))
Numerical answer
[src]
x1 = 4.71238898038469 - 1.76274717403909*i
x2 = -1.5707963267949 + 1.76274717403909*i
x2 = -1.5707963267949 + 1.76274717403909*i
The graph