Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x^2-8*x+17=0
-
Equation -x/12+x=55/12
-
Equation 4-6(x+2)=3-5x
-
Equation (x+2)/9=(x-3)/2
- Express {x} in terms of y where:
- -4*x+6*y=-7
- 2*x+3*y=14
- 18*x-8*y=-2
- -11*x+15*y=7
- Derivative of:
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tanx/2
- Integral of d{x}:
-
tanx/2
-
Identical expressions
- tanx/ two =√ three / two
- tangent of x divide by 2 equally √3 divide by 2
- tangent of x divide by two equally √ three divide by two
- tanx divide by 2=√3 divide by 2
-
Similar expressions
- o=o*x^6-3*sqrt(x)+x^3*tan(x)-x*(x^3*tan(x)/2+2*x^2*tan(x)^(2/3)+x*tan(x)-x+1)+3*x-1
- asin(y/3)=Const+atan(x/2)/2
- -tan(x/2)=1/2*ln(2)
- tan(x/2)=-√3/3
tanx/2=√3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ tan(x) \/ 3 ------ = ----- 2 2
$$\frac{\tan{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\frac{\tan{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
The equation is transformed to
$$\tan{\left(x \right)} = \sqrt{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
$$\frac{\tan{\left(x \right)}}{2} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
Divide both parts of the equation by 1/2
The equation is transformed to
$$\tan{\left(x \right)} = \sqrt{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi
0 + --
3
$$0 + \frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
product
pi 1*-- 3
$$1 \frac{\pi}{3}$$
=
pi -- 3
$$\frac{\pi}{3}$$
pi/3
Numerical answer
[src]
x1 = 51.3126800086333
x2 = 4.18879020478639
x3 = 98.4365698124802
x4 = 48.1710873550435
x5 = -71.2094334813686
x6 = 67.0206432765823
x7 = 41.8879020478639
x8 = -49.2182849062401
x9 = 29.3215314335047
x10 = -61.7846555205993
x11 = 32.4631240870945
x12 = -27.2271363311115
x13 = -5.23598775598299
x14 = 16.7551608191456
x15 = 85.870199198121
x16 = -64.9262481741891
x17 = 70.162235930172
x18 = 79.5870138909414
x19 = -46.0766922526503
x20 = -90.0589894029074
x21 = 38.7463093942741
x22 = 73.3038285837618
x23 = 57.5958653158129
x24 = 82.7286065445312
x25 = -20.943951023932
x26 = 92.1533845053006
x27 = 7.33038285837618
x28 = -33.5103216382911
x29 = 76.4454212373516
x30 = -8.37758040957278
x31 = -39.7935069454707
x32 = -74.3510261349584
x33 = -99.4837673636768
x34 = -77.4926187885482
x35 = -55.5014702134197
x36 = 60.7374579694027
x37 = -96.342174710087
x38 = -86.9173967493176
x39 = -80.634211442138
x40 = 10.471975511966
x41 = -17.8023583703422
x42 = 26.1799387799149
x43 = -93.2005820564972
x44 = -14.6607657167524
x45 = -30.3687289847013
x46 = -2.0943951023932
x47 = -11.5191730631626
x48 = -68.0678408277789
x49 = -83.7758040957278
x50 = 23.0383461263252
x51 = 1.0471975511966
x52 = 13.6135681655558
x53 = 19.8967534727354
x54 = -42.9350995990605
x55 = -58.6430628670095
x56 = -24.0855436775217
x57 = -36.6519142918809
x58 = 54.4542726622231
x59 = 101.57816246607
x60 = -52.3598775598299
x61 = 45.0294947014537
x62 = 35.6047167406843
x63 = 95.2949771588904
x64 = 63.8790506229925
x64 = 63.8790506229925
The graph