Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation |x|=-2
- Equation x+y-3=0
-
Equation 2^x=6-x
-
Equation 80-x=9*5
- Express {x} in terms of y where:
- 7*x-2*y=18
- -1*x-6*y=18
- 6*x-19*y=-18
- 10*x-5*y=3
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Identical expressions
- two *sin(x)-sqrt(three)= zero
- 2 multiply by sinus of (x) minus square root of (3) equally 0
- two multiply by sinus of (x) minus square root of (three) equally zero
- 2*sin(x)-√(3)=0
- 2sin(x)-sqrt(3)=0
- 2sinx-sqrt3=0
- 2*sin(x)-sqrt(3)=O
-
Similar expressions
- (2-3x-2x^2)(2sin(x)-sqrt3)=0
- 2*sin(x)+sqrt(3)=0
- 2*sinx-sqrt(3)=0
2*sin(x)-sqrt(3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$2 \sin{\left(x \right)} - \sqrt{3} = 0$$
- this is the simplest trigonometric equation
We get:
$$2 \sin{\left(x \right)} = \sqrt{3}$$
The equation is transformed to
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
$$2 \sin{\left(x \right)} - \sqrt{3} = 0$$
- 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:
$$2 \sin{\left(x \right)} = \sqrt{3}$$
Divide both parts of the equation by 2
The equation is transformed to
$$\sin{\left(x \right)} = \frac{\sqrt{3}}{2}$$
This equation is transformed to
$$x = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$x = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$x = 2 \pi n + \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Sum and product of roots
[src]
sum
pi 2*pi -- + ---- 3 3
$$\frac{\pi}{3} + \frac{2 \pi}{3}$$
=
pi
$$\pi$$
product
pi 2*pi --*---- 3 3
$$\frac{\pi}{3} \frac{2 \pi}{3}$$
=
2 2*pi ----- 9
$$\frac{2 \pi^{2}}{9}$$
2*pi^2/9
Rapid solution
[src]
pi
x1 = --
3
$$x_{1} = \frac{\pi}{3}$$
2*pi
x2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
x2 = 2*pi/3
Numerical answer
[src]
x1 = -79.5870138909414
x2 = -35.6047167406843
x3 = 27.2271363311115
x4 = -4.18879020478639
x5 = 146.607657167524
x6 = -93.2005820564972
x7 = -5.23598775598299
x8 = 240.855436775217
x9 = 90.0589894029074
x10 = -85.870199198121
x11 = -73.3038285837618
x12 = 209.43951023932
x13 = 33.5103216382911
x14 = -36.6519142918809
x15 = 70.162235930172
x16 = -104.71975511966
x17 = 76.4454212373516
x18 = -92.1533845053006
x19 = 95.2949771588904
x20 = 39.7935069454707
x21 = -61.7846555205993
x22 = 38.7463093942741
x23 = -17.8023583703422
x24 = 8.37758040957278
x25 = -613.657765001206
x26 = -49.2182849062401
x27 = -99.4837673636768
x28 = 170.693200845045
x29 = -30.3687289847013
x30 = 195.825942073764
x31 = -60.7374579694027
x32 = -42.9350995990605
x33 = 14.6607657167524
x34 = 46.0766922526503
x35 = -11.5191730631626
x36 = 45.0294947014537
x37 = 89.0117918517108
x38 = -86.9173967493176
x39 = -6607.81654805053
x40 = 944.572191179331
x41 = 51.3126800086333
x42 = 19.8967534727354
x43 = 1188.56922060814
x44 = 63.8790506229925
x45 = 52.3598775598299
x46 = 77.4926187885482
x47 = 64.9262481741891
x48 = 71.2094334813686
x49 = 101.57816246607
x50 = 1.0471975511966
x51 = -68.0678408277789
x52 = -16.7551608191456
x53 = 20.943951023932
x54 = -54.4542726622231
x55 = -10.471975511966
x56 = -67.0206432765823
x57 = -41.8879020478639
x58 = -24.0855436775217
x59 = 2.0943951023932
x60 = -520.457182944709
x61 = -74.3510261349584
x62 = -23.0383461263252
x63 = 57.5958653158129
x64 = 32.4631240870945
x65 = 96.342174710087
x66 = 26.1799387799149
x67 = -98.4365698124802
x68 = 13.6135681655558
x69 = -29.3215314335047
x70 = -112.050137978036
x71 = 83.7758040957278
x72 = 58.6430628670095
x73 = -55.5014702134197
x74 = 82.7286065445312
x75 = -80.634211442138
x76 = 7.33038285837618
x77 = -48.1710873550435
x77 = -48.1710873550435
The graph