Mister Exam
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How to use it?
- Equation:
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Equation 2*sin(x)=0
-
Equation (x-5)^2-x^2=3
-
Equation -2*(-y-2)-y-2=0
-
Equation x^2+x=6
- Express {x} in terms of y where:
- -6*x+15*y=-13
- -17*x+14*y=11
- -11*x-3*y=-15
- 9*x-6*y=-20
-
Identical expressions
- tg(17x)=sqrt three /3
- tg(17x) equally square root of 3 divide by 3
- tg(17x) equally square root of three divide by 3
- tg(17x)=√3/3
- tg17x=sqrt3/3
- tg(17x)=sqrt3 divide by 3
-
Similar expressions
- tg(\pi(4x-4))/(6)=(\sqrt(3))/(3)
- 3/((2sin^3(pi+x))+(sqrt(3)/4cos^2(pi/2-x)))-4/(2cos(3pi/2-x)+sqrt(3)/3sin^2(pi+x))=0
- (2*sqrt(3))/(3*x+81)=13
tg(17x)=sqrt3/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
\/ 3
tan(17*x) = -----
3
$$\tan{\left(17 x \right)} = \frac{\sqrt{3}}{3}$$
Detail solution
Given the equation
$$\tan{\left(17 x \right)} = \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$17 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$17 x = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$17$$
we get the answer:
$$x_{1} = \frac{\pi n}{17} + \frac{\pi}{102}$$
$$\tan{\left(17 x \right)} = \frac{\sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$17 x = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$17 x = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$17$$
we get the answer:
$$x_{1} = \frac{\pi n}{17} + \frac{\pi}{102}$$
Sum and product of roots
[src]
sum
pi --- 102
$$\frac{\pi}{102}$$
=
pi --- 102
$$\frac{\pi}{102}$$
product
pi --- 102
$$\frac{\pi}{102}$$
=
pi --- 102
$$\frac{\pi}{102}$$
pi/102
Numerical answer
[src]
x1 = 53.9922737425775
x2 = 66.004245653362
x3 = 86.1473985499083
x4 = 62.3082542961976
x5 = -54.6698721580577
x6 = -81.6506090653583
x7 = -41.7339024079821
x8 = 8.53158004945463
x9 = 46.2306918925322
x10 = 72.2874309605416
x11 = -36.0051158043771
x12 = -15.8619629078308
x13 = 96.3113747821106
x14 = 28.3051338102845
x15 = -95.6953762225832
x16 = 89.6585903392146
x17 = -70.0082362902902
x18 = -45.9842924687212
x19 = 82.2666076248857
x20 = -63.7250509831106
x21 = 58.2426638033167
x22 = -65.7578462295511
x23 = 70.2546357141012
x24 = 87.9953942284906
x25 = 6.31398523515596
x26 = -7.730781922069
x27 = -13.8291676613904
x28 = -31.754725743638
x29 = -55.778669565207
x30 = 50.2962823854131
x31 = -28.0587343864735
x32 = 80.2338123784452
x33 = -89.7817900511201
x34 = -29.7219304971976
x35 = -2.00199531846408
x36 = 2.24839474227505
x37 = -87.7489948046796
x38 = -11.9811719828081
x39 = 22.0219485031049
x40 = 34.2187199817476
x41 = 94.2785795356702
x42 = -49.6802838258857
x43 = -99.7609667154641
x44 = -21.775549079294
x45 = 18.1411575780822
x46 = 4.2811899887155
x47 = 60.2754590497571
x48 = -37.8531114829594
x49 = 32.001125167449
x50 = 0.58519863155104
x51 = 48.2634871389726
x52 = -19.7427538328535
x53 = 103.518557928581
x54 = -97.7281714690237
x55 = -85.7161995582392
x56 = 16.2931618995
x57 = -27.6891352507571
x58 = -17.7099585864131
x59 = -57.9962643795057
x60 = -77.7698181403356
x61 = 38.2843104746286
x62 = 56.025068989018
x63 = 78.0162175641465
x64 = -79.9874129546343
x65 = 12.2275714066191
x66 = 14.2603666530596
x67 = -53.7458743187666
x68 = 52.1442780639953
x69 = -3.84999099704632
x70 = 42.3499009675095
x71 = 19.9891532566645
x72 = 36.2515152281881
x73 = 26.2723385638441
x74 = 41.0563039925019
x75 = -67.9754410438497
x76 = 24.2395433174036
x77 = 76.1682218855643
x78 = -61.6922557366702
x79 = -51.7130790723261
x80 = 10.0099765923204
x81 = 40.317105721069
x82 = 68.2218404676607
x83 = 63.7866508390633
x84 = -91.2601865939858
x85 = 100.007366139275
x86 = -47.8322881473034
x87 = -91.9993848654187
x88 = -73.7042276474547
x89 = -39.7011071615416
x90 = 84.2994028713261
x91 = 92.2457842892297
x92 = 74.3202262069821
x93 = 44.0130970782335
x94 = -23.9931438935926
x95 = -9.76357716850946
x96 = -43.7666976544225
x97 = -83.6834043117987
x98 = -71.8562319688724
x99 = -75.7370228938951
x100 = -5.69798667562855
x100 = -5.69798667562855