Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 6/(x-2)+5/x=3
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Equation sin(x)=4
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Equation 9^x-8*3^x-9=0
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Equation x^2-6x-27=0
- Express {x} in terms of y where:
- 16*x-17*y=-15
- -4*x-4*y=19
- 15*x+1*y=19
- -16*x-10*y=4
- 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)= four
- sinus of (x) equally 4
- sinus of (x) equally four
- sinx=4
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Similar expressions
- sin(x/2+pi/6)=1
- 30*(sinx-0.125*cosx)=10.9
- sinx=4
sin(x)=4 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(x \right)} = 4$$
- 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.
$$\sin{\left(x \right)} = 4$$
- 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(4)) - I*im(asin(4))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}$$
x2 = I*im(asin(4)) + re(asin(4))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}$$
x2 = re(asin(4)) + i*im(asin(4))
Sum and product of roots
[src]
sum
pi - re(asin(4)) - I*im(asin(4)) + I*im(asin(4)) + re(asin(4))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(4)) - I*im(asin(4)))*(I*im(asin(4)) + re(asin(4)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
=
-(I*im(asin(4)) + re(asin(4)))*(-pi + I*im(asin(4)) + re(asin(4)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(4 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(4 \right)}\right)}\right)$$
-(i*im(asin(4)) + re(asin(4)))*(-pi + i*im(asin(4)) + re(asin(4)))
Numerical answer
[src]
x1 = 1.5707963267949 + 2.06343706889556*i
x2 = 1.5707963267949 - 2.06343706889556*i
x2 = 1.5707963267949 - 2.06343706889556*i
The graph