Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation x^2-5x+4=0
-
Equation (11x+14)-(5x-8)=25
-
Equation -25-x=-17
- Equation x^2-10*x-24=0
- Express {x} in terms of y where:
- -14*x+10*y=19
- 19*x-12*y=16
- -6*x+12*y=11
- -9*x-1*y=6
- Derivative of:
-
tg(3x)
- Integral of d{x}:
- tg(3x)
-
Identical expressions
- tg(three x)=3^(one / two)
- tg(3x) equally 3 to the power of (1 divide by 2)
- tg(three x) equally 3 to the power of (one divide by two)
- tg(3x)=3(1/2)
- tg3x=31/2
- tg3x=3^1/2
- tg(3x)=3^(1 divide by 2)
-
Similar expressions
- 2tg^3x-2tg^2x+3tgx-3=0
- tg3x+tgx=1
- -0.1*x-arctg(3*x)-arctg(0.6*x)=-pi/2
- tg2x-ctg3x=0
tg(3x)=3^(1/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(3 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$3 x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{9}$$
$$\tan{\left(3 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{atan}{\left(\sqrt{3} \right)}$$
Or
$$3 x = \pi n + \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{9}$$
Sum and product of roots
[src]
sum
pi -- 9
$$\frac{\pi}{9}$$
=
pi -- 9
$$\frac{\pi}{9}$$
product
pi -- 9
$$\frac{\pi}{9}$$
=
pi -- 9
$$\frac{\pi}{9}$$
pi/9
Numerical answer
[src]
x1 = -57.246799465414
x2 = -77.1435529381494
x3 = -97.0403064108847
x4 = -1.74532925199433
x5 = -81.3323431429358
x6 = -43.6332312998582
x7 = -87.6155284501153
x8 = 90.4080552533063
x9 = -55.1524043630208
x10 = 78.8888821901437
x11 = 30.7177948351002
x12 = -41.538836197465
x13 = -74.0019602845596
x14 = 35.9537825910832
x15 = 18.151424220741
x16 = 48.5201532054424
x17 = -31.0668606854991
x18 = 2.44346095279206
x19 = -30.0196631343025
x20 = 50.6145483078356
x21 = -52.010811709431
x22 = -83.4267382453289
x23 = 26.5290046303138
x24 = 86.2192650485199
x25 = 52.7089434102288
x26 = -93.8987137572949
x27 = 13.9626340159546
x28 = -23.7364778271229
x29 = 100.880030765272
x30 = -25.8308729295161
x31 = 32.8121899374934
x32 = -53.0580092606276
x33 = 42.2369678982628
x34 = 76.7944870877505
x35 = -45.7276264022514
x36 = 40.1425727958696
x37 = 0.349065850398866
x38 = 4.53785605518526
x39 = 12.915436464758
x40 = 16.0570291183478
x41 = -91.8043186549017
x42 = -59.3411945678072
x43 = -19.5476876223365
x44 = -39.4444410950718
x45 = -71.9075651821664
x46 = 20.2458193231342
x47 = -95.9931088596881
x48 = 34.9065850398866
x49 = 92.5024503556995
x50 = -69.8131700797732
x51 = 60.0393262686049
x52 = 28.623399732707
x53 = 38.0481776934764
x54 = -15.3588974175501
x55 = -17.4532925199433
x56 = 54.8033385126219
x57 = -21.6420827247297
x58 = -47.8220215046446
x59 = -67.71877497738
x60 = 82.0304748437335
x61 = 44.331363000656
x62 = -11.1701072127637
x63 = -79.2379480405426
x64 = -27.9252680319093
x65 = -99.1347015132779
x66 = 64.2281164733913
x67 = 70.5113017805709
x68 = 56.8977336150151
x69 = -61.4355896702004
x70 = 68.4169066781777
x71 = 8.72664625997165
x72 = 72.6056968829641
x73 = 74.7000919853573
x74 = -8.02851455917392
x75 = -5.93411945678072
x76 = 62.1337213709981
x77 = -37.3500459926787
x78 = -63.5299847725936
x79 = 57.9449311662117
x80 = -75.0491578357562
x81 = -85.5211333477222
x82 = 96.6912405604859
x83 = -35.2556508902855
x84 = -49.9164166070378
x85 = -65.6243798749868
x86 = 98.7856356628791
x87 = 10.8210413623648
x88 = -33.1612557878923
x89 = 46.4257581030492
x90 = 24.4346095279206
x91 = 94.5968454580927
x92 = -3.83972435438753
x93 = -13.2645023151569
x94 = 88.3136601509131
x95 = 6.63225115757845
x96 = -89.7099235525085
x97 = 22.3402144255274
x98 = 66.3225115757845
x99 = 84.1248699461267
x99 = 84.1248699461267