Mister Exam
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How to use it?
- Equation:
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Equation (y^4+4*y^2-12)/4=0
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Equation x^2-3x-10=0
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Equation (x-119)/(x+7)=-5
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Equation 5(x-2)^2=-6x-44
- Express {x} in terms of y where:
- -2*x-15*y=-1
- 10*x-2*y=11
- 11*x-2*y=-9
- 13*x-18*y=-17
- Graphing y =:
- 2*sin(x/2)
- Derivative of:
-
2*sin(x/2)
- Limit of the function:
- -sqrt(3)
-
Identical expressions
- two *sin(x/ two)=-sqrt(three)
- 2 multiply by sinus of (x divide by 2) equally minus square root of (3)
- two multiply by sinus of (x divide by two) equally minus square root of (three)
- 2*sin(x/2)=-√(3)
- 2sin(x/2)=-sqrt(3)
- 2sinx/2=-sqrt3
- 2*sin(x divide by 2)=-sqrt(3)
-
Similar expressions
- 2*sin(x)/(2+3)=0
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- Sqrt(2(sin(x/2*(1-cos(x)))^2))=-sin(-x)-5cos(x)
- 2sin*x/2=sqrt3
- 2*sin(x/2)=+sqrt(3)
- sqrt(2(sinx/2)^2)-sinx=0
2*sin(x/2)=-sqrt(3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x\ ___
2*sin|-| = -\/ 3
\2/
$$2 \sin{\left(\frac{x}{2} \right)} = - \sqrt{3}$$
Detail solution
Given the equation
$$2 \sin{\left(\frac{x}{2} \right)} = - \sqrt{3}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\sin{\left(\frac{x}{2} \right)} = - \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{3}$$
$$\frac{x}{2} = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \frac{2 \pi}{3}$$
$$x_{2} = 4 \pi n + \frac{8 \pi}{3}$$
$$2 \sin{\left(\frac{x}{2} \right)} = - \sqrt{3}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(\frac{x}{2} \right)} = - \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$\frac{x}{2} = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$\frac{x}{2} = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$\frac{x}{2} = 2 \pi n - \frac{\pi}{3}$$
$$\frac{x}{2} = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 4 \pi n - \frac{2 \pi}{3}$$
$$x_{2} = 4 \pi n + \frac{8 \pi}{3}$$
Sum and product of roots
[src]
sum
2*pi 8*pi - ---- + ---- 3 3
$$- \frac{2 \pi}{3} + \frac{8 \pi}{3}$$
=
2*pi
$$2 \pi$$
product
-2*pi 8*pi -----*---- 3 3
$$- \frac{2 \pi}{3} \frac{8 \pi}{3}$$
=
2 -16*pi ------- 9
$$- \frac{16 \pi^{2}}{9}$$
-16*pi^2/9
Rapid solution
[src]
-2*pi
x1 = -----
3
$$x_{1} = - \frac{2 \pi}{3}$$
8*pi
x2 = ----
3
$$x_{2} = \frac{8 \pi}{3}$$
x2 = 8*pi/3
Numerical answer
[src]
x1 = -16.7551608191456
x2 = -54.4542726622231
x3 = 85.870199198121
x4 = 73.3038285837618
x5 = -41.8879020478639
x6 = 83.7758040957278
x7 = 33.5103216382911
x8 = 8.37758040957278
x9 = -27.2271363311115
x10 = -77.4926187885482
x11 = -90.0589894029074
x12 = 35.6047167406843
x13 = 48.1710873550435
x14 = -29.3215314335047
x15 = -102.625360017267
x16 = -366.519142918809
x17 = 10.471975511966
x18 = 58.6430628670095
x19 = -67.0206432765823
x20 = 1843.06769010601
x21 = 46.0766922526503
x22 = -14.6607657167524
x23 = -4.18879020478639
x24 = -39.7935069454707
x25 = -64.9262481741891
x26 = 272.271363311115
x27 = -2.0943951023932
x28 = -79.5870138909414
x29 = -44700.674670378
x30 = 71.2094334813686
x31 = 20.943951023932
x32 = -203.15632493214
x33 = 23.0383461263252
x34 = -92.1533845053006
x35 = 96.342174710087
x36 = -52.3598775598299
x37 = 60.7374579694027
x38 = 98.4365698124802
x38 = 98.4365698124802