Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation (x-4)^2+(x+9)^2=2*x^2
-
Equation sin(x)=-1/4
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Equation tg(x)=-1/2
- Equation sqrt(x-2sqrt(x-1))+sqrt(x+2sqrt(x-1))=x-1
- Express {x} in terms of y where:
- 14*x-16*y=14
- -10*x+18*y=6
- 4*x+13*y=13
- 17*x-19*y=1
- Derivative of:
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tg(x)
- -1/2
- Graphing y =:
- tg(x)
- Integral of d{x}:
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tg(x)
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-1/2
- Limit of the function:
- -1/2
-
Identical expressions
- tg(x)=- one / two
- tg(x) equally minus 1 divide by 2
- tg(x) equally minus one divide by two
- tgx=-1/2
- tg(x)=-1 divide by 2
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Similar expressions
- ctg((x-pi)/4)-1=0
- tg(x)=+1/2
- 2/tg^2x+7/tgx+5=0
- 1-e^(-n*(n-1)/(2*4096))=3/4
- (sqrt3*tgx+1)/(2*sinx-1)=0
- ((49^tg^2x)/7^2sqtr3tgx)=8
tg(x)=-1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
$$\tan{\left(x \right)} = - \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \frac{1}{2} \right)}$$
Or
$$x = \pi n - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
product
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
=
-atan(1/2)
$$- \operatorname{atan}{\left(\frac{1}{2} \right)}$$
-atan(1/2)
Rapid solution
[src]
x1 = -atan(1/2)
$$x_{1} = - \operatorname{atan}{\left(\frac{1}{2} \right)}$$
x1 = -atan(1/2)
Numerical answer
[src]
x1 = -9.88842556977019
x2 = -63.2955006807967
x3 = 27.8106862733073
x4 = 100.067317305873
x5 = -79.0034639487456
x6 = -3.6052402625906
x7 = 87.5009466915134
x8 = -53.8707227200273
x9 = -69.5786859879763
x10 = -0.463647609000806
x11 = 43.5186495412563
x12 = -88.428241909515
x13 = 74.9345760771542
x14 = 56.0850201556155
x15 = -19.3132035305396
x16 = 12.1027230053584
x17 = 18.385908312538
x18 = -44.4459447592579
x19 = 59.2266128092053
x20 = 90.6425393451032
x21 = 78.076168730744
x22 = 2.67794504458899
x23 = -66.4370933343865
x24 = -85.2866492559252
x25 = -97.8530198702844
x26 = -16.1716108769498
x27 = 71.7929834235644
x28 = -60.1539080272069
x29 = 93.784131998693
x30 = -25.5963888377192
x31 = -47.5875374128477
x32 = -31.8795741448987
x33 = -22.4547961841294
x34 = 49.8018348484359
x35 = 40.3770568876665
x36 = 15.2443156589482
x37 = 37.2354642340767
x38 = 5.81953769817878
x39 = 65.5097981163849
x40 = 34.0938715804869
x41 = 68.6513907699746
x42 = -72.7202786415661
x43 = -57.0123153736171
x44 = 30.9522789268971
x45 = -100.994612523874
x46 = 8.96113035176857
x47 = 46.6602421948461
x48 = -50.7291300664375
x49 = -35.0211667984885
x50 = 24.6690936197175
x51 = -94.7114272166946
x52 = -82.1450566023354
x53 = -41.3043521056681
x54 = 62.3682054627951
x55 = -6.74683291618039
x56 = 52.9434275020257
x57 = 21.5275009661277
x58 = 81.2177613843338
x59 = -28.7379814913089
x60 = 96.9257246522828
x61 = -75.8618712951559
x62 = -91.5698345631048
x63 = -38.1627594520783
x64 = 84.3593540379236
x65 = -13.03001822336
x65 = -13.03001822336
The graph