Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2*x^2+6*x+9=0
-
Equation cos(x)=(1/2)
-
Equation (x^2-4)^2+(x^2-6*x-16)^2=0
-
Equation 3x^2-5x-2=0
- Express {x} in terms of y where:
- 17*x-18*y=10
- 9*x-4*y=2
- -16*x-20*y=6
- 20*x+6*y=8
- Derivative of:
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tg(x)
-
1/2
- Graphing y =:
- tg(x)
- Integral of d{x}:
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tg(x)
-
1/2
- Sum of series:
-
1/2
-
Identical expressions
- tg(x)= one / two
- tg(x) equally 1 divide by 2
- tg(x) equally one divide by two
- tgx=1/2
- tg(x)=1 divide by 2
-
Similar expressions
- (cosx-1)(tgx+√3)√cosx=0
- tgx-3^(1/2)*ctgx=3^(1/2)-1
tg(x)=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
$$\tan{\left(x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
Or
$$x = \pi n + \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
atan(1/2)
$$\operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
atan(1/2)
$$\operatorname{atan}{\left(\frac{1}{2} \right)}$$
product
atan(1/2)
$$\operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
atan(1/2)
$$\operatorname{atan}{\left(\frac{1}{2} \right)}$$
atan(1/2)
Rapid solution
[src]
x1 = atan(1/2)
$$x_{1} = \operatorname{atan}{\left(\frac{1}{2} \right)}$$
x1 = atan(1/2)
Numerical answer
[src]
x1 = -15.2443156589482
x2 = 3.6052402625906
x3 = -43.5186495412563
x4 = -68.6513907699746
x5 = 0.463647609000806
x6 = -34.0938715804869
x7 = 13.03001822336
x8 = 35.0211667984885
x9 = -46.6602421948461
x10 = -65.5097981163849
x11 = -81.2177613843338
x12 = 75.8618712951559
x13 = 16.1716108769498
x14 = 47.5875374128477
x15 = 88.428241909515
x16 = 63.2955006807967
x17 = -71.7929834235644
x18 = 57.0123153736171
x19 = 28.7379814913089
x20 = -96.9257246522828
x21 = 6.74683291618039
x22 = 97.8530198702844
x23 = -37.2354642340767
x24 = 69.5786859879763
x25 = 82.1450566023354
x26 = -8.96113035176857
x27 = 38.1627594520783
x28 = -100.067317305873
x29 = 44.4459447592579
x30 = -62.3682054627951
x31 = 25.5963888377192
x32 = 66.4370933343865
x33 = -93.784131998693
x34 = -59.2266128092053
x35 = -74.9345760771542
x36 = -18.385908312538
x37 = 41.3043521056681
x38 = 19.3132035305396
x39 = -49.8018348484359
x40 = -2.67794504458899
x41 = 50.7291300664375
x42 = 9.88842556977019
x43 = -52.9434275020257
x44 = 85.2866492559252
x45 = -84.3593540379236
x46 = 31.8795741448987
x47 = 79.0034639487456
x48 = 94.7114272166946
x49 = 100.994612523874
x50 = 22.4547961841294
x51 = -24.6690936197175
x52 = -30.9522789268971
x53 = -40.3770568876665
x54 = -21.5275009661277
x55 = -78.076168730744
x56 = -5.81953769817878
x57 = 91.5698345631048
x58 = 60.1539080272069
x59 = -27.8106862733073
x60 = -12.1027230053584
x61 = -56.0850201556155
x62 = -87.5009466915134
x63 = -90.6425393451032
x64 = 53.8707227200273
x65 = 72.7202786415661
x65 = 72.7202786415661
The graph