Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation 2x=18-x
-
Equation x^4=(2*x-3)^2
-
Equation 9*x^2=54*x
-
Equation cos(x)+sin(x)=0
- Express {x} in terms of y where:
- -18*x-1*y=-11
- 7*x-2*y=20
- -1*x-20*y=-17
- -2*x-14*y=7
- Derivative of:
-
tg3x
- Graphing y =:
- tg3x
- Integral of d{x}:
-
tg3x
-
Identical expressions
- tg three x=-√ three /3
- tg3x equally minus √3 divide by 3
- tg three x equally minus √ three divide by 3
- tg3x=-√3 divide by 3
-
Similar expressions
- 3tg^3x+3tg^2x+3tgx+1=0
- tg(3x)=3^(1/2)
- tg3x=+√3/3
tg3x=-√3/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
tan(3*x) = -------
3
$$\tan{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$3 x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{18}$$
$$\tan{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(- \frac{\sqrt{3}}{3} \right)}$$
Or
$$3 x = \pi n - \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{18}$$
Sum and product of roots
[src]
sum
-pi ---- 18
$$- \frac{\pi}{18}$$
=
-pi ---- 18
$$- \frac{\pi}{18}$$
product
-pi ---- 18
$$- \frac{\pi}{18}$$
=
-pi ---- 18
$$- \frac{\pi}{18}$$
-pi/18
Numerical answer
[src]
x1 = 78.3652834145454
x2 = -13.7881010907552
x3 = -96.5167076352864
x4 = -94.4223125328932
x5 = -75.5727566113545
x6 = -42.0624349730633
x7 = 65.7989128001862
x8 = 76.2708883121522
x9 = 80.4596785169386
x10 = 59.5157274930066
x11 = -51.4872129338327
x12 = 19.7222205475359
x13 = -20.0712863979348
x14 = 63.704517697793
x15 = -68.2423737529783
x16 = 28.0998009571087
x17 = 34.3829862642883
x18 = 36.4773813666815
x19 = -61.9591884457987
x20 = 54.2797397370236
x21 = -35.7792496658838
x22 = 30.1941960595019
x23 = -11.693705988362
x24 = -97.563905186483
x25 = 74.176493209759
x26 = 45.9021593274509
x27 = -44.1568300754565
x28 = -15.8824961931484
x29 = 61.6101225953998
x30 = 56.3741348394168
x31 = -81.8559419185341
x32 = 21.8166156499291
x33 = 87.7900613753148
x34 = -53.5816080362259
x35 = -0.174532925199433
x36 = -92.3279174305
x37 = -9.59931088596881
x38 = 96.1676417848876
x39 = 94.0732466824944
x40 = 83.6012711705284
x41 = -31.5904594610974
x42 = -64.0535835481919
x43 = 47.9965544298441
x44 = 26.0054058547155
x45 = 81.5068760681352
x46 = -59.8647933434055
x47 = 8.20304748437335
x48 = 1.91986217719376
x49 = 6.10865238198015
x50 = 85.6956662729216
x51 = -99.6583002888762
x52 = -26.3544717051144
x53 = -4.36332312998582
x54 = -70.3367688553715
x55 = 4.01425727958696
x56 = -72.4311639577647
x57 = 72.0820981073658
x58 = -77.6671517137477
x59 = -29.4960643587042
x60 = -74.5255590601579
x61 = 50.0909495322373
x62 = -55.6760031386191
x63 = 15.5334303427495
x64 = 58.46852994181
x65 = 12.3918376891597
x66 = -90.2335223281068
x67 = -79.7615468161409
x68 = -17.9768912955416
x69 = -37.873644768277
x70 = 98.2620368872808
x71 = 14.4862327915529
x72 = -46.2512251778497
x73 = -66.1479786505851
x74 = -88.1391272257137
x75 = 67.8933079025794
x76 = -6.45771823237902
x77 = 52.1853446346305
x78 = -22.165681500328
x79 = 69.9877030049726
x80 = -39.9680398706701
x81 = 23.9110107523223
x82 = -83.9503370209273
x83 = 43.8077642250577
x84 = -28.4488668075076
x85 = 32.2885911618951
x86 = 39.6189740202713
x87 = 89.884456477708
x88 = -86.0447321233204
x89 = 91.9788515801012
x90 = 37.5245789178781
x91 = -33.6848545634906
x92 = -24.2600766027212
x93 = 41.7133691226645
x94 = 10.2974425867665
x95 = -2.26892802759263
x96 = -57.7703982410123
x97 = 17.6278254451427
x98 = 100.356431989674
x99 = -48.3456202802429
x100 = -50.4400153826361
x101 = -7.50491578357562
x101 = -7.50491578357562