Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 81*x^3+18*x^2+x=0
-
Equation (-x-4)*(3*x+3)=0
- Equation x^2-144=0
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Equation -x=5
- Express {x} in terms of y where:
- -2*x-19*y=3
- 15*x+10*y=-4
- 15*x+9*y=5
- -9*x+5*y=-2
- Integral of d{x}:
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sinx/2
- Derivative of:
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sinx/2
- Graphing y =:
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sinx/2
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Identical expressions
- sinx/ two = eight
- sinus of x divide by 2 equally 8
- sinus of x divide by two equally eight
- sinx divide by 2=8
-
Similar expressions
- sin(x/2)=-1/2
- 2*sin(x/2-pi/6)=1
- Sqrt(2(sin(x/2*(1-cos(x)))^2))=-sin(-x)-5cos(x)
- sin(x)/(cos(x/2)^(2))=4*sin(x/2)^(2)
sinx/2=8 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\frac{\sin{\left(x \right)}}{2} = 8$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(x \right)} = 16$$
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.
$$\frac{\sin{\left(x \right)}}{2} = 8$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/2
The equation is transformed to
$$\sin{\left(x \right)} = 16$$
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 - re(asin(16)) - I*im(asin(16)) + I*im(asin(16)) + re(asin(16))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(16)) - I*im(asin(16)))*(I*im(asin(16)) + re(asin(16)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}\right)$$
=
-(I*im(asin(16)) + re(asin(16)))*(-pi + I*im(asin(16)) + re(asin(16)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}\right)$$
-(i*im(asin(16)) + re(asin(16)))*(-pi + i*im(asin(16)) + re(asin(16)))
Rapid solution
[src]
x1 = pi - re(asin(16)) - I*im(asin(16))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}$$
x2 = I*im(asin(16)) + re(asin(16))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(16 \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(16 \right)}\right)}$$
x2 = re(asin(16)) + i*im(asin(16))
Numerical answer
[src]
x1 = 1.5707963267949 + 3.46475790667586*i
x2 = 1.5707963267949 - 3.46475790667586*i
x2 = 1.5707963267949 - 3.46475790667586*i