Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation 7*x=0
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Equation 3x-2=x+4
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Equation tan(x)=7
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Equation (x-3)(x^2-2x+1)=3(x-1)
- Express {x} in terms of y where:
- 18*x-10*y=-9
- 18*x-12*y=-9
- 12*x+11*y=20
- 19*x-12*y=-9
- Graphing y =:
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tan(x/2)
- Integral of d{x}:
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tan(x/2)
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sqrt(3)
- Limit of the function:
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tan(x/2)
- Derivative of:
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sqrt(3)
- The double integral of:
- sqrt(3)
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Identical expressions
- tan(x/ two)=sqrt(three)
- tangent of (x divide by 2) equally square root of (3)
- tangent of (x divide by two) equally square root of (three)
- tan(x/2)=√(3)
- tanx/2=sqrt3
- tan(x divide by 2)=sqrt(3)
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Similar expressions
- tan(x)/2=cot(x)/2
tan(x/2)=sqrt(3) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(\frac{x}{2} \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{2 \pi}{3}$$
$$\tan{\left(\frac{x}{2} \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{x}{2} = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$\frac{x}{2} = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{1}{2}$$
we get the answer:
$$x_{1} = 2 \pi n + \frac{2 \pi}{3}$$
Sum and product of roots
[src]
sum
2*pi ---- 3
$$\frac{2 \pi}{3}$$
=
2*pi ---- 3
$$\frac{2 \pi}{3}$$
product
2*pi ---- 3
$$\frac{2 \pi}{3}$$
=
2*pi ---- 3
$$\frac{2 \pi}{3}$$
2*pi/3
Numerical answer
[src]
x1 = -67.0206432765823
x2 = 8.37758040957278
x3 = -41.8879020478639
x4 = -79.5870138909414
x5 = 2.0943951023932
x6 = -35.6047167406843
x7 = -23.0383461263252
x8 = 102.625360017267
x9 = 27.2271363311115
x10 = -4.18879020478639
x11 = -60.7374579694027
x12 = 52.3598775598299
x13 = 90.0589894029074
x14 = -85.870199198121
x15 = 96.342174710087
x16 = -73.3038285837618
x17 = 77.4926187885482
x18 = 64.9262481741891
x19 = 71.2094334813686
x20 = -98.4365698124802
x21 = 33.5103216382911
x22 = -29.3215314335047
x23 = 83.7758040957278
x24 = 58.6430628670095
x25 = -92.1533845053006
x26 = 14.6607657167524
x27 = 46.0766922526503
x28 = -16.7551608191456
x29 = 39.7935069454707
x30 = 20.943951023932
x31 = -54.4542726622231
x32 = -48.1710873550435
x33 = -10.471975511966
x33 = -10.471975511966
The graph