Mister Exam
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How to use it?
- Equation:
-
Equation ctg3x=-√3/3
- Equation log3(x2–3x–5)=log3(7–2x)
- Equation (x^2-16):(x^3+3x^2+16)=0
-
Equation 836-16*m=420
- Express {x} in terms of y where:
- 60x^2y+75x^2y^2+120xy^260x2y+75x2y2+120xy2приx=-0,5x=−0,5,y=0,4y=0,4.
- (x-17)^2+(y+26)^2=16(x−17)2+(y+26)2=16.
- 5*x-5*y=20
- 8*x-7*y=-13
- Integral of d{x}:
- ctg3x
- Derivative of:
-
ctg3x
-
Identical expressions
- ctg three x=-√ three /3
- ctg3x equally minus √3 divide by 3
- ctg three x equally minus √ three divide by 3
- ctg3x=-√3 divide by 3
-
Similar expressions
- arctg(x-1)+arctg(x)+arctg(x+1)=arctg(3x)
- (0,5*x)*arctg(3*x)+(0,3*x)*arctg(x)=-pi+pi/4
- ctg3x=+√3/3
- arcctg(3x^2-1)=arcctg(2x^2+x+1)
- tan(x/3)=-(√3/3)
- ctg(3x-2)=1
ctg3x=-√3/3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
cot(3*x) = -------
3
$$\cot{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
Detail solution
Given the equation
$$\cot{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{acot}{\left(- \frac{\sqrt{3}}{3} \right)}$$
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:
$$x_{1} = \frac{\pi n}{3} - \frac{\pi}{9}$$
$$\cot{\left(3 x \right)} = \frac{\left(-1\right) \sqrt{3}}{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x = \pi n + \operatorname{acot}{\left(- \frac{\sqrt{3}}{3} \right)}$$
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 = -19.1986217719376
x2 = -21.2930168743308
x3 = -87.2664625997165
x4 = 78.190750489346
x5 = 69.8131700797732
x6 = -95.6440430092893
x7 = 49.9164166070378
x8 = -9.77384381116824
x9 = -62.1337213709981
x10 = 14.3116998663535
x11 = 3.83972435438753
x12 = 66.6715774261834
x13 = 46.774823953448
x14 = -40.1425727958696
x15 = -45.3785605518526
x16 = -73.6528944341607
x17 = -57.9449311662117
x18 = -91.4552528045029
x19 = 90.7571211037051
x20 = 64.5771823237902
x21 = -1.39626340159546
x22 = -11.8682389135614
x23 = 98.0875039620813
x24 = 12.2173047639603
x25 = -5.58505360638185
x26 = 25.8308729295161
x27 = 80.2851455917392
x28 = 54.1052068118242
x29 = -82.0304748437335
x30 = 95.9931088596881
x31 = -43.2841654494594
x32 = 74.0019602845596
x33 = -89.3608577021097
x34 = 86.5683308989187
x35 = -79.9360797413403
x36 = -51.6617458590322
x37 = -23.387411976724
x38 = 5.93411945678072
x39 = -38.0481776934764
x40 = 27.9252680319093
x41 = -85.1720674973233
x42 = -60.0393262686049
x43 = 52.010811709431
x44 = -99.8328332140756
x45 = 16.4060949687467
x46 = 47.8220215046446
x47 = -67.3697091269811
x48 = -71.5584993317675
x49 = 88.6627260013119
x50 = 2.79252680319093
x51 = 100.181899064475
x52 = 24.7836753783195
x53 = -3.49065850398866
x54 = 71.9075651821664
x55 = 40.4916386462684
x56 = 76.0963553869528
x57 = 82.3795406941324
x58 = -69.4641042293743
x59 = -31.7649923862968
x60 = 10.1229096615671
x61 = -41.1897703470662
x62 = -25.4818070791172
x63 = 84.4739357965256
x64 = 22.6892802759263
x65 = -35.9537825910832
x66 = -7.67944870877505
x67 = -97.7384381116825
x68 = -75.7472895365539
x69 = -18.151424220741
x70 = -49.567350756639
x71 = -33.85938748869
x72 = 62.482787221397
x73 = 91.8043186549017
x74 = -16.0570291183478
x75 = 68.7659725285766
x76 = 42.5860337486616
x77 = 38.3972435438752
x78 = -55.8505360638185
x79 = 58.2939970166106
x80 = 34.2084533390889
x81 = -47.4729556542458
x82 = -93.5496479068961
x83 = 60.3883921190038
x84 = 32.1140582366957
x85 = 8.02851455917392
x86 = 36.3028484414821
x87 = -13.9626340159546
x88 = -77.8416846389471
x89 = 44.6804288510548
x90 = 18.5004900711399
x91 = -27.5762021815104
x92 = -84.1248699461267
x93 = -53.7561409614254
x94 = -29.6705972839036
x95 = 56.1996019142174
x96 = -63.1809189221947
x97 = 20.5948851735331
x98 = 93.8987137572949
x99 = 30.0196631343025
x100 = -65.2753140245879
x100 = -65.2753140245879
The graph