Mister Exam
Other calculators
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How to use it?
- Equation:
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Equation cos(x)-1=0
- Equation 64-x^2=0
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Equation sin(5*x)=-1
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Equation 7^x-2=49
- Express {x} in terms of y where:
- -17*x+9*y=-1
- -19*x-18*y=6
- -20*x+14*y=7
- -4*x-18*y=-8
-
Identical expressions
- tg* two x=2
- tg multiply by 2x equally 2
- tg multiply by two x equally 2
- tg2x=2
-
Similar expressions
- tg^2*x/2
- 2-1/ctg^2x=0
- tg2x=3tgx
- -x-arctg(2*x)=-3,14
tg*2x=2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(2 x \right)} = 2$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Or
$$2 x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\operatorname{atan}{\left(2 \right)}}{2}$$
$$\tan{\left(2 x \right)} = 2$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(2 \right)}$$
Or
$$2 x = \pi n + \operatorname{atan}{\left(2 \right)}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\operatorname{atan}{\left(2 \right)}}{2}$$
Rapid solution
[src]
atan(2)
x1 = -------
2
$$x_{1} = \frac{\operatorname{atan}{\left(2 \right)}}{2}$$
x1 = atan(2)/2
Sum and product of roots
[src]
sum
atan(2) ------- 2
$$\frac{\operatorname{atan}{\left(2 \right)}}{2}$$
=
atan(2) ------- 2
$$\frac{\operatorname{atan}{\left(2 \right)}}{2}$$
product
atan(2) ------- 2
$$\frac{\operatorname{atan}{\left(2 \right)}}{2}$$
=
atan(2) ------- 2
$$\frac{\operatorname{atan}{\left(2 \right)}}{2}$$
atan(2)/2
Numerical answer
[src]
x1 = -23.0083705430264
x2 = -71.7030566736682
x3 = 99.5137429469755
x4 = 72.8102053914623
x5 = -66.9906676932835
x6 = 20.9739266072307
x7 = 64.9562237574878
x8 = -16.7251852358468
x9 = -41.8579264645652
x10 = -161.238447300977
x11 = -74.844649327258
x12 = 94.8013539665908
x13 = 129.358873156079
x14 = -43.4287227913601
x15 = 85.3765760058215
x16 = 52.3898531431286
x17 = 86.9473723326164
x18 = 49.2482604895388
x19 = 27.2571119144103
x20 = -77.9862419808478
x21 = -99.9773905559763
x22 = 30.3987045680001
x23 = -81.1278346344376
x24 = 96.3721502933857
x25 = 93.2305576397959
x26 = 97.9429466201806
x27 = 3.69516701248684
x28 = -5.72961094828254
x29 = -55.9950934057192
x30 = -85.8402236148223
x31 = 13.1199449732562
x32 = 90.0889649862062
x33 = -44.999519118155
x34 = -34.0039448305907
x35 = -19.8667778894366
x36 = 42.9650751823593
x37 = -57.5658897325141
x38 = -27.7207595234111
x39 = 9.97835231966642
x40 = -48.1411117717447
x41 = -84.2694272880274
x42 = -63.8490750396937
x43 = -451.835767758033
x44 = 60.2438347771031
x45 = 24.1155192608205
x46 = 31.969500894795
x47 = -4.15881462148764
x48 = 33.5402972215899
x49 = 16.261537626846
x50 = 5.26596333928174
x51 = -49.7119080985396
x52 = 71.2394090646674
x53 = -79.5570383076427
x54 = 2.12437068569194
x55 = -88.9818162684121
x56 = 38.2526862019746
x57 = 8.40755599287153
x58 = 35.1110935483848
x59 = -125.110131784695
x60 = -90.552612595207
x61 = 53.9606494699235
x62 = -21.4375742162315
x63 = 74.3810017182572
x64 = 14.6907413000511
x65 = -93.6942052487967
x66 = 41.3942788555644
x67 = 46.106667835949
x68 = -13.583592582257
x69 = -1.01722196789785
x70 = 82.2349833522317
x71 = 75.9517980450521
x72 = -12.0127962554621
x73 = -68.5614640200784
x74 = -24.5791668698213
x75 = 68.0978164110776
x76 = -52.8535007521294
x77 = -59.136686059309
x78 = -35.5747411573856
x78 = -35.5747411573856