Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+10)^2=(5-x)^2
-
Equation sin(x)=-1/4
-
Equation 3x-3=7x-3(2x-5)
-
Equation k^2-2*k+1=0
- Express {x} in terms of y where:
- 9*x-18*y=6
- -10*x+18*y=6
- 17*x-19*y=1
- -1*x+19*y=-10
-
Identical expressions
- tg(five *x+pi/ three)= one /√ three
- tg(5 multiply by x plus Pi divide by 3) equally 1 divide by √3
- tg(five multiply by x plus Pi divide by three) equally one divide by √ three
- tg(5x+pi/3)=1/√3
- tg5x+pi/3=1/√3
- tg(5*x+pi divide by 3)=1 divide by √3
-
Similar expressions
- tg(5*x-pi/3)=1/√3
- sin(x/2)*cos(3x/2)-1/√(3)*sin(2x)=sin(3x/2)*cos(x/2)
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What you mean?
- tan((5*x + pi)/3) = 1/sqrt(3)
- tan(5*(x + pi)/3) = 1/sqrt(3)
- tan(5*x + pi/3) = 1/sqrt(3)
- tan(5*x + pi/3) = 1/sqrt(3)
You entered:
tg(5*x+pi/3)=1/√3
What you mean?
tg(5*x+pi/3)=1/√3 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ pi\ 1
tan|5*x + --| = 1*-----
\ 3 / ___
\/ 3
$$\tan{\left(5 x + \frac{\pi}{3} \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
Detail solution
Given the equation
$$\tan{\left(5 x + \frac{\pi}{3} \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x + \frac{\pi}{3} = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$5 x + \frac{\pi}{3} = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$5 x = \pi n - \frac{\pi}{6}$$
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{\pi n}{5} - \frac{\pi}{30}$$
$$\tan{\left(5 x + \frac{\pi}{3} \right)} = 1 \cdot \frac{1}{\sqrt{3}}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x + \frac{\pi}{3} = \pi n + \operatorname{atan}{\left(\frac{\sqrt{3}}{3} \right)}$$
Or
$$5 x + \frac{\pi}{3} = \pi n + \frac{\pi}{6}$$
, where n - is a integer
Move
$$\frac{\pi}{3}$$
to right part of the equation
with the opposite sign, in total:
$$5 x = \pi n - \frac{\pi}{6}$$
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{\pi n}{5} - \frac{\pi}{30}$$
Sum and product of roots
[src]
sum
pi
0 - --
30
$$- \frac{\pi}{30} + 0$$
=
-pi ---- 30
$$- \frac{\pi}{30}$$
product
-pi 1*---- 30
$$1 \left(- \frac{\pi}{30}\right)$$
=
-pi ---- 30
$$- \frac{\pi}{30}$$
-pi/30
Numerical answer
[src]
x1 = 52.0457182944709
x2 = -59.7949801733257
x3 = -81.7861287484543
x4 = 90.3731486682664
x5 = -41.5737427825049
x6 = -49.7418836818384
x7 = 66.497044500984
x8 = 26.2846585350346
x9 = -71.733032256967
x10 = -66.0781654805053
x11 = -67.9631210726592
x12 = -89.9542696477877
x13 = 84.0899633610868
x14 = 70.2669556852917
x15 = -78.0162175641465
x16 = 41.9926218029836
x17 = -19.5825942073764
x18 = 53.9306738866248
x19 = 46.3908515180093
x20 = 16.2315620435473
x21 = -100.007366139275
x22 = 14.3466064513934
x23 = -73.6179878491208
x24 = 82.2050077689329
x25 = 30.0545697193424
x26 = 40.1076662108297
x27 = -57.9100245811719
x28 = -91.8392252399416
x29 = -9.52949771588904
x30 = -45.9719724975306
x31 = 92.2581042604203
x32 = 20.001473227855
x33 = 75.9218224617533
x34 = 72.1519112774456
x35 = -21.4675497995303
x36 = -27.7507351067098
x37 = 88.4881930761125
x38 = 96.028015444728
x39 = 100.426245159754
x40 = 94.1430598525741
x41 = 18.1165176357011
x42 = -29.6356906988637
x43 = 8.0634211442138
x44 = 24.3997029428807
x45 = -12.0427718387609
x46 = -23.9808239224021
x47 = 0.523598775598299
x48 = -25.865779514556
x49 = -1.98967534727354
x50 = -93.7241808320955
x51 = -83.6710843406082
x52 = 68.3820000931378
x53 = 34.4527994343681
x54 = -39.6887871903511
x55 = 63.9837703781121
x56 = -7.64454212373516
x57 = 80.320052176779
x58 = -35.9188760060433
x59 = -43.4586983746588
x60 = -13.9277274309148
x61 = 28.1696141271885
x62 = -31.5206462910176
x63 = 22.5147473507269
x64 = 4.29350995990605
x65 = 31.9395253114962
x66 = 56.4439480094966
x67 = 62.0988147859582
x68 = -85.556039932762
x69 = -17.6976386152225
x70 = -97.4940920164032
x71 = 6.17846555205993
x72 = 50.160762702317
x73 = 2.40855436775218
x74 = -75.5029434412747
x75 = 12.4616508592395
x76 = 48.2758071101632
x77 = -61.6799357654796
x78 = 44.5058959258554
x79 = -63.5648913576335
x80 = -47.8569280896845
x81 = -37.8038315981972
x82 = 85.9749189532407
x83 = -15.8126830230686
x84 = 36.3377550265219
x85 = -69.8480766648131
x86 = 58.3289036016505
x87 = 74.0368668695995
x88 = -88.0693140556339
x89 = -79.9011731563004
x90 = -51.6268392739923
x91 = 78.4350965846252
x92 = 60.2138591938044
x93 = -53.5117948661461
x94 = -34.0339204138894
x95 = -3.87463093942741
x96 = -56.025068989018
x97 = 98.5412895675998
x98 = 38.2227106186758
x99 = -95.6091364242494
x100 = 9.94837673636768
x101 = -5.75958653158129
x101 = -5.75958653158129
The graph