Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (|x+4|)=5
-
Equation -2*x-4=3*x
-
Equation x^2+4*x+3=0
-
Equation x^4-2*x^3+x^2-1=0
- Express {x} in terms of y where:
- 6*x-19*y=-18
- 15*x+1*y=19
- -2*x+2*y=4
- 10*x+3*y=2
- Integral of d{x}:
-
sqrt(3)
- Derivative of:
-
sqrt(3)
- The double integral of:
- sqrt(3)
-
Identical expressions
- tg three *x=sqrt(3)
- tg3 multiply by x equally square root of (3)
- tg three multiply by x equally square root of (3)
- tg3*x=√(3)
- tg3x=sqrt(3)
- tg3x=sqrt3
-
Similar expressions
- (tg(5x)-tg(3x))/(1+tg(5x)tg(3x))=sqrt(3)
- tgx-1/3×tg^3x-1/5×tg^5x=0
- sin(x)+sqrt3*cosx=2sin2x
- tg2x-ctg3x=0
- tg(3*x)+tg(x)=1
tg3*x=sqrt(3) 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
$$\left(\frac{\pi}{9}\right)$$
=
pi -- 9
$$\frac{\pi}{9}$$
product
pi -- 9
$$\left(\frac{\pi}{9}\right)$$
=
pi -- 9
$$\frac{\pi}{9}$$
Numerical answer
[src]
x1 = -91.8043186549017
x2 = 24.4346095279206
x3 = 50.6145483078356
x4 = -33.1612557878923
x5 = 35.9537825910832
x6 = -87.6155284501153
x7 = -97.0403064108847
x8 = 12.915436464758
x9 = -19.5476876223365
x10 = -83.4267382453289
x11 = 10.8210413623648
x12 = -63.5299847725936
x13 = 78.8888821901437
x14 = 100.880030765272
x15 = -89.7099235525085
x16 = -95.9931088596881
x17 = 88.3136601509131
x18 = -3.83972435438753
x19 = -37.3500459926787
x20 = 16.0570291183478
x21 = 32.8121899374934
x22 = -79.2379480405426
x23 = -21.6420827247297
x24 = -43.6332312998582
x25 = 52.7089434102288
x26 = -17.4532925199433
x27 = 13.9626340159546
x28 = -27.9252680319093
x29 = -77.1435529381494
x30 = 40.1425727958696
x31 = -99.1347015132779
x32 = -85.5211333477222
x33 = -1.74532925199433
x34 = 26.5290046303138
x35 = -25.8308729295161
x36 = -59.3411945678072
x37 = -57.246799465414
x38 = 82.0304748437335
x39 = 72.6056968829641
x40 = 86.2192650485199
x41 = -67.71877497738
x42 = 44.331363000656
x43 = -93.8987137572949
x44 = -55.1524043630208
x45 = -23.7364778271229
x46 = 56.8977336150151
x47 = 57.9449311662117
x48 = -15.3588974175501
x49 = 76.7944870877505
x50 = 96.6912405604859
x51 = -49.9164166070378
x52 = 2.44346095279206
x53 = -11.1701072127637
x54 = 46.4257581030492
x55 = -61.4355896702004
x56 = 30.7177948351002
x57 = 66.3225115757845
x58 = -71.9075651821664
x59 = 92.5024503556995
x60 = -53.0580092606276
x61 = 94.5968454580927
x62 = 20.2458193231342
x63 = 22.3402144255274
x64 = -69.8131700797732
x65 = 68.4169066781777
x66 = -75.0491578357562
x67 = -30.0196631343025
x68 = 74.7000919853573
x69 = 98.7856356628791
x70 = -35.2556508902855
x71 = -41.538836197465
x72 = -39.4444410950718
x73 = 28.623399732707
x74 = 34.9065850398866
x75 = 18.151424220741
x76 = -65.6243798749868
x77 = -81.3323431429358
x78 = -74.0019602845596
x79 = -5.93411945678072
x80 = 0.349065850398866
x81 = -52.010811709431
x82 = 4.53785605518526
x83 = -8.02851455917392
x84 = 90.4080552533063
x85 = 6.63225115757845
x86 = 62.1337213709981
x87 = 42.2369678982628
x88 = 38.0481776934764
x89 = 64.2281164733913
x90 = -47.8220215046446
x91 = -31.0668606854991
x92 = -13.2645023151569
x93 = 54.8033385126219
x94 = -45.7276264022514
x95 = 84.1248699461267
x96 = 48.5201532054424
x97 = 60.0393262686049
x98 = 8.72664625997165
x99 = 70.5113017805709
x99 = 70.5113017805709
The graph