Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 2x-5=7
-
Equation log(x)+1=0
- Equation -4/9y=16/27
- Equation tg(x)+sqrt(3)=0
- Express {x} in terms of y where:
- -4*x+20*y=10
- -16*x-7*y=-5
- -13*x+7*y=11
- -11*x+4*y=-20
-
Identical expressions
- tg(x)+sqrt(three)= zero
- tg(x) plus square root of (3) equally 0
- tg(x) plus square root of (three) equally zero
- tg(x)+√(3)=0
- tgx+sqrt3=0
- tg(x)+sqrt(3)=O
-
Similar expressions
- 3*tg*x+sqrt3=0
- tg(x)-sqrt(3)=0
tg(x)+sqrt(3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\tan{\left(x \right)} + \sqrt{3} = 0$$
- this is the simplest trigonometric equation
We get:
$$\tan{\left(x \right)} = - \sqrt{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Or
$$x = \pi n - \frac{\pi}{3}$$
, where n - is a integer
$$\tan{\left(x \right)} + \sqrt{3} = 0$$
- this is the simplest trigonometric equation
Move sqrt(3) to right part of the equation
with the change of sign in sqrt(3)
We get:
$$\tan{\left(x \right)} = - \sqrt{3}$$
This equation is transformed to
$$x = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Or
$$x = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Sum and product of roots
[src]
sum
-pi ---- 3
$$- \frac{\pi}{3}$$
=
-pi ---- 3
$$- \frac{\pi}{3}$$
product
-pi ---- 3
$$- \frac{\pi}{3}$$
=
-pi ---- 3
$$- \frac{\pi}{3}$$
-pi/3
Numerical answer
[src]
x1 = 30.3687289847013
x2 = 20.943951023932
x3 = -85.870199198121
x4 = 36.6519142918809
x5 = -92.1533845053006
x6 = 55.5014702134197
x7 = 64.9262481741891
x8 = -79.5870138909414
x9 = -54.4542726622231
x10 = 74.3510261349584
x11 = -29.3215314335047
x12 = -51.3126800086333
x13 = -45.0294947014537
x14 = 52.3598775598299
x15 = 99.4837673636768
x16 = 77.4926187885482
x17 = -19.8967534727354
x18 = -13.6135681655558
x19 = 61.7846555205993
x20 = 11.5191730631626
x21 = 93.2005820564972
x22 = 33.5103216382911
x23 = 27.2271363311115
x24 = 80.634211442138
x25 = 14.6607657167524
x26 = -67.0206432765823
x27 = -38.7463093942741
x28 = -76.4454212373516
x29 = 39.7935069454707
x30 = -95.2949771588904
x31 = -23.0383461263252
x32 = -57.5958653158129
x33 = 24.0855436775217
x34 = 5.23598775598299
x35 = -32.4631240870945
x36 = -63.8790506229925
x37 = -26.1799387799149
x38 = -70.162235930172
x39 = -60.7374579694027
x40 = -16.7551608191456
x41 = 58.6430628670095
x42 = -10.471975511966
x43 = 46.0766922526503
x44 = -48.1710873550435
x45 = -98.4365698124802
x46 = -73.3038285837618
x47 = -4.18879020478639
x48 = -101.57816246607
x49 = 2.0943951023932
x50 = 17.8023583703422
x51 = -7.33038285837618
x52 = 49.2182849062401
x53 = -89.0117918517108
x54 = 8.37758040957278
x55 = 83.7758040957278
x56 = 96.342174710087
x57 = -1.0471975511966
x58 = 71.2094334813686
x59 = 68.0678408277789
x60 = -35.6047167406843
x61 = 90.0589894029074
x62 = -41.8879020478639
x63 = -82.7286065445312
x64 = 42.9350995990605
x64 = 42.9350995990605