Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation -x^2-4*x-3=0
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Equation 3x+3=-2-7x
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Equation sin(-x)=0
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Equation (x+3)^3=81*(x+3)
- Express {x} in terms of y where:
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Identical expressions
- two *sin(x)- three = zero
- 2 multiply by sinus of (x) minus 3 equally 0
- two multiply by sinus of (x) minus three equally zero
- 2sin(x)-3=0
- 2sinx-3=0
- 2*sin(x)-3=O
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Similar expressions
- 2*sin(x-(3/5))-(3/2)+x=0
- (sin^2)-(2*(sin*x))-3=0
- 2*sin(x)+3=0
- 2*sinx-3=0
2*sin(x)-3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(x \right)} - 3 = 0$$
- this is the simplest trigonometric equation
We get:
$$2 \sin{\left(x \right)} = 3$$
The equation is transformed to
$$\sin{\left(x \right)} = \frac{3}{2}$$
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.
$$2 \sin{\left(x \right)} - 3 = 0$$
- this is the simplest trigonometric equation
Move -3 to right part of the equation
with the change of sign in -3
We get:
$$2 \sin{\left(x \right)} = 3$$
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(x \right)} = \frac{3}{2}$$
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(3/2)) - I*im(asin(3/2))
$$x_{1} = - \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}$$
x2 = I*im(asin(3/2)) + re(asin(3/2))
$$x_{2} = \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}$$
x2 = re(asin(3/2)) + i*im(asin(3/2))
Sum and product of roots
[src]
sum
pi - re(asin(3/2)) - I*im(asin(3/2)) + I*im(asin(3/2)) + re(asin(3/2))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) + \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)$$
=
pi
$$\pi$$
product
(pi - re(asin(3/2)) - I*im(asin(3/2)))*(I*im(asin(3/2)) + re(asin(3/2)))
$$\left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(- \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + \pi - i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)$$
=
-(I*im(asin(3/2)) + re(asin(3/2)))*(-pi + I*im(asin(3/2)) + re(asin(3/2)))
$$- \left(\operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right) \left(- \pi + \operatorname{re}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)} + i \operatorname{im}{\left(\operatorname{asin}{\left(\frac{3}{2} \right)}\right)}\right)$$
-(i*im(asin(3/2)) + re(asin(3/2)))*(-pi + i*im(asin(3/2)) + re(asin(3/2)))
Numerical answer
[src]
x1 = 1.5707963267949 + 0.962423650119207*i
x2 = 1.5707963267949 - 0.962423650119207*i
x2 = 1.5707963267949 - 0.962423650119207*i
The graph