Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation sin^2x=1/2
-
Equation tg2x-1=0
-
Equation sin(8*x-pi/3)=0
-
Equation (7-2x)(9-2x)-35=0
- Express {x} in terms of y where:
- 5*x-5*y=20
- 8*x-7*y=-13
- 15*x-15*y=16
- 9*x+18*y=6
-
Identical expressions
- tg2x- one = zero
- tg2x minus 1 equally 0
- tg2x minus one equally zero
- tg2x-1=O
-
Similar expressions
- 3(tg^2(x)-1)*sqrt(-5cosx)=0
- (cos2x+1)tg^2x-1=0
- tg^2(x-1)=0
- tg2x+1=0
tg2x-1=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(2 x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move $-1$ to right part of the equation
with the change of sign in $-1$
We get:
$$\tan{\left(2 x \right)} - 1 + 1 = 1$$
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
$$\tan{\left(2 x \right)} - 1 = 0$$
- this is the simplest trigonometric equation
Move $-1$ to right part of the equation
with the change of sign in $-1$
We get:
$$\tan{\left(2 x \right)} - 1 + 1 = 1$$
This equation is transformed to
$$2 x = \pi n + \operatorname{atan}{\left(1 \right)}$$
Or
$$2 x = \pi n + \frac{\pi}{4}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{8}$$
Sum and product of roots
[src]
sum
pi -- 8
$$\left(\frac{\pi}{8}\right)$$
=
pi -- 8
$$\frac{\pi}{8}$$
product
pi -- 8
$$\left(\frac{\pi}{8}\right)$$
=
pi -- 8
$$\frac{\pi}{8}$$
Numerical answer
[src]
x1 = -100.138265833175
x2 = 5.10508806208341
x3 = -89.1426915456104
x4 = 20.8130513300324
x5 = -82.8595062384308
x6 = -16.8860605130451
x7 = 66.3661448070844
x8 = 80.5033117482384
x9 = 38.0918109247762
x10 = 41.233403578366
x11 = 14.5298660228528
x12 = 72.649330114264
x13 = 96.2112750161874
x14 = -64.009950316892
x15 = 30.2378292908018
x16 = -13.7444678594553
x17 = 56.941366846315
x18 = -96.9966731795849
x19 = 67.9369411338793
x20 = -37.3064127613788
x21 = -51.4435797025329
x22 = 89.9280897090078
x23 = -68.7223392972767
x24 = 74.2201264410589
x25 = 93.0696823625976
x26 = -24.7400421470196
x27 = -87.5718952188155
x28 = -15.3152641862502
x29 = 8.24668071567321
x30 = 71.0785337874691
x31 = 31.8086256175967
x32 = -53.0143760293278
x33 = -7.46128255227576
x34 = 6.67588438887831
x35 = -93.8550805259951
x36 = -46.7311907221482
x37 = 16.1006623496477
x38 = 45.9457925587507
x39 = -56.1559686829176
x40 = 12.9590696960579
x41 = 94.6404786893925
x42 = -79.717913584841
x43 = -1.17809724509617
x44 = -75.0055246044563
x45 = -60.8683576633022
x46 = 63.2245521534946
x47 = 23.9546439836222
x48 = -34.164820107789
x49 = 27.096236637212
x50 = -49.872783375738
x51 = 49.0873852123405
x52 = 82.0741080750334
x53 = 34.9502182711865
x54 = -95.42587685279
x55 = 42.8041999051609
x56 = -90.7134878724053
x57 = 50.6581815391354
x58 = 44.3749962319558
x59 = 58.5121631731099
x60 = -42.0188017417635
x61 = -20.0276531666349
x62 = -71.8639319508665
x63 = 0.392699081698724
x64 = 19.2422550032375
x65 = -43.5895980685584
x66 = 28.6670329640069
x67 = 60.0829594999048
x68 = -73.4347282776614
x69 = -67.1515429704818
x70 = -38.8772090881737
x71 = -2.74889357189107
x72 = -9.03207887907065
x73 = 97.7820713429823
x74 = 64.7953484802895
x75 = 53.7997741927252
x76 = -35.7356164345839
x77 = 85.2157007286231
x78 = 86.786497055418
x79 = -65.5807466436869
x80 = -27.8816348006094
x81 = 88.3572933822129
x82 = -45.1603943953533
x83 = 78.9325154214436
x84 = -5.89048622548086
x85 = -81.2887099116359
x86 = 1.96349540849362
x87 = -21.5984494934298
x88 = -86.0010988920206
x89 = -57.7267650097125
x90 = -29.4524311274043
x91 = 100.923663996572
x92 = 75.7909227678538
x93 = -23.1692458202247
x94 = 36.5210145979813
x95 = -12.1736715326604
x96 = 22.3838476568273
x97 = 52.2289778659303
x98 = 9.8174770424681
x99 = -31.0232274541992
x100 = -59.2975613365073
x101 = -78.1471172580461
x101 = -78.1471172580461
The graph