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- Equation:
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Equation tg(3x+(pi)/6)=1
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Identical expressions
- tg(3x+(pi)/ six)= one
- tg(3x plus ( Pi ) divide by 6) equally 1
- tg(3x plus ( Pi ) divide by six) equally one
- tg3x+pi/6=1
- tg(3x+(pi) divide by 6)=1
-
Similar expressions
- tg(3x-(pi)/6)=1
tg(3x+(pi)/6)=1 equation
The teacher will be very surprised to see your correct solution 😉
The solution
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[src]
/ pi\ tan|3*x + --| = 1 \ 6 /
$$\tan{\left(3 x + \frac{\pi}{6} \right)} = 1$$
Detail solution
Given the equation
$$\tan{\left(3 x + \frac{\pi}{6} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$3 x + \frac{\pi}{6} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$3 x = \pi n + \frac{\pi}{12}$$
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{36}$$
$$\tan{\left(3 x + \frac{\pi}{6} \right)} = 1$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x + \frac{\pi}{6} = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$3 x + \frac{\pi}{6} = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$3 x = \pi n + \frac{\pi}{12}$$
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{36}$$
Sum and product of roots
[src]
sum
pi
0 + --
36
$$0 + \frac{\pi}{36}$$
=
pi -- 36
$$\frac{\pi}{36}$$
product
pi 1*-- 36
$$1 \frac{\pi}{36}$$
=
pi -- 36
$$\frac{\pi}{36}$$
pi/36
Numerical answer
[src]
x1 = 63.9663170855922
x2 = 98.5238362750799
x3 = -19.8094870101356
x4 = -77.4053523259485
x5 = -87.8773278379145
x6 = 19.9840199353351
x7 = -17.7150919077424
x8 = -35.5174502780846
x9 = 56.635934227216
x10 = 10.5592419745657
x11 = -75.3109572235553
x12 = 52.4471440224296
x13 = -89.9717229403077
x14 = -41.8006355852642
x15 = -4.10152374218667
x16 = 30.4559954473011
x17 = -23.998277214922
x18 = 82.8158730071309
x19 = -21.9038821125288
x20 = -31.3286600732982
x21 = 44.0695636128568
x22 = 16.8424272817453
x23 = -33.4230551756914
x24 = 34.6447856520874
x25 = 68.1551072903786
x26 = 24.1728101401215
x27 = 74.4382925975582
x28 = -85.7829327355213
x29 = 22.0784150377283
x30 = 80.7214779047377
x31 = 50.3527489200364
x32 = 0.0872664625997165
x33 = -93.1133155938975
x34 = 36.7391807544806
x35 = 100.618231377473
x36 = -5.14872129338327
x37 = -15.6206968053492
x38 = -37.6118453804778
x39 = 70.2495023927718
x40 = -51.2254135460336
x41 = 66.0607121879854
x42 = -43.8950306876574
x43 = -26.0926723173152
x44 = -65.8861792627859
x45 = 6.3704517697793
x46 = 17.8896248329419
x47 = 90.1462558655071
x48 = 41.9751685104636
x49 = -81.5941425307349
x50 = 58.7303293296092
x51 = 2.18166156499291
x52 = -79.4997474283417
x53 = 94.3350460702935
x54 = -53.3198086484268
x55 = 88.0518607631139
x56 = 28.3616003449079
x57 = 76.5326876999514
x58 = 38.8335758568738
x59 = -57.5085988532132
x60 = -63.7917841603927
x61 = 84.9102681095241
x62 = 39.8807734080704
x63 = -59.6029939556064
x64 = 54.5415391248228
x65 = -45.9894257900506
x66 = -99.3965009010771
x67 = -67.9805743651791
x68 = 92.2406509679003
x69 = -61.6973890579996
x70 = -2.00712863979348
x71 = 32.5503905496942
x72 = 85.9574656607207
x73 = 4.27605666738611
x74 = 60.8247244320024
x75 = 48.2583538176432
x76 = -70.0749694675723
x77 = -92.0661180427009
x78 = -55.41420375082
x79 = 78.6270828023445
x80 = 96.4294411726867
x81 = -27.1398698685118
x82 = -29.234264970905
x83 = 12.6536370769589
x84 = -13.5263017029561
x85 = 8.4648468721725
x86 = 46.16395871525
x87 = -95.2077106962907
x88 = -48.0838208924438
x89 = -49.1310184436404
x90 = -11.4319066005629
x91 = -73.2165621211621
x92 = 26.2672052425147
x93 = 14.7480321793521
x94 = 72.343897495165
x95 = -97.3021057986839
x96 = -71.1221670187689
x97 = -9.33751149816966
x98 = -39.706240482871
x99 = 61.871921983199
x100 = -7.24311639577647
x101 = -83.6885376331281
x101 = -83.6885376331281
The graph