Mister Exam
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Identical expressions
- tg(x/ two)-√ three = zero
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Similar expressions
- tg(x/2)+√3=0
tg(x/2)-√3=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/x\ ___ tan|-| - \/ 3 = 0 \2/
$$\tan{\left(\frac{x}{2} \right)} - \sqrt{3} = 0$$
Detail solution
Given the equation
$$\tan{\left(\frac{x}{2} \right)} - \sqrt{3} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(\frac{x}{2} \right)} = \sqrt{3}$$
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:
$$x_{1} = 2 \pi n + \frac{2 \pi}{3}$$
$$\tan{\left(\frac{x}{2} \right)} - \sqrt{3} = 0$$
- this is the simplest trigonometric equation
Move -sqrt(3) to right part of the equation
with the change of sign in -sqrt(3)
We get:
$$\tan{\left(\frac{x}{2} \right)} = \sqrt{3}$$
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 = -29.3215314335047
x2 = 96.342174710087
x3 = -92.1533845053006
x4 = -41.8879020478639
x5 = -35.6047167406843
x6 = -10.471975511966
x7 = -67.0206432765823
x8 = 33.5103216382911
x9 = 71.2094334813686
x10 = -60.7374579694027
x11 = -79.5870138909414
x12 = -48.1710873550435
x13 = -85.870199198121
x14 = 39.7935069454707
x15 = 102.625360017267
x16 = 20.943951023932
x17 = 2.0943951023932
x18 = 64.9262481741891
x19 = -23.0383461263252
x20 = 14.6607657167524
x21 = 83.7758040957278
x22 = 8.37758040957278
x23 = 90.0589894029074
x24 = 27.2271363311115
x25 = -98.4365698124802
x26 = 58.6430628670095
x27 = 77.4926187885482
x28 = -73.3038285837618
x29 = -54.4542726622231
x30 = 46.0766922526503
x31 = 52.3598775598299
x32 = -4.18879020478639
x33 = -16.7551608191456
x33 = -16.7551608191456