Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/12+x/8+x=-29/6
-
Equation x^2+7x-18=0
- Equation x-y+2=0
-
Equation x^2-2x=0
- Express {x} in terms of y where:
- 13*x-18*y=-17
- 7*x+6*y=20
- -7*x-19*y=-18
- 5*x+12*y=18
-
Identical expressions
- two *sin(x)+sqrt(three)= zero
- 2 multiply by sinus of (x) plus square root of (3) equally 0
- two multiply by sinus of (x) plus 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*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
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, 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
$$x = 2 \pi n - \frac{\pi}{3}$$
$$x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Rapid solution
[src]
-pi
x1 = ----
3
$$x_{1} = - \frac{\pi}{3}$$
4*pi
x2 = ----
3
$$x_{2} = \frac{4 \pi}{3}$$
x2 = 4*pi/3
Sum and product of roots
[src]
sum
pi 4*pi - -- + ---- 3 3
$$- \frac{\pi}{3} + \frac{4 \pi}{3}$$
=
pi
$$\pi$$
product
-pi 4*pi ----*---- 3 3
$$- \frac{\pi}{3} \frac{4 \pi}{3}$$
=
2 -4*pi ------ 9
$$- \frac{4 \pi^{2}}{9}$$
-4*pi^2/9
Numerical answer
[src]
x1 = -32.4631240870945
x2 = -33.5103216382911
x3 = -77.4926187885482
x4 = -63.8790506229925
x5 = 393.746279249921
x6 = 49.2182849062401
x7 = 92.1533845053006
x8 = -82.7286065445312
x9 = -14.6607657167524
x10 = -13.6135681655558
x11 = 68.0678408277789
x12 = 5.23598775598299
x13 = 23.0383461263252
x14 = -26.1799387799149
x15 = -7.33038285837618
x16 = -20.943951023932
x17 = 41.8879020478639
x18 = -1559.27715373173
x19 = -46.0766922526503
x20 = -11851.1346868919
x21 = -90.0589894029074
x22 = 74.3510261349584
x23 = 67.0206432765823
x24 = 54.4542726622231
x25 = -114.144533080429
x26 = 73.3038285837618
x27 = 35.6047167406843
x28 = -76.4454212373516
x29 = 98.4365698124802
x30 = 60.7374579694027
x31 = -83.7758040957278
x32 = -71.2094334813686
x33 = 85.870199198121
x34 = 10.471975511966
x35 = -8.37758040957278
x36 = 30.3687289847013
x37 = -27.2271363311115
x38 = 36.6519142918809
x39 = -96.342174710087
x40 = -19.8967534727354
x41 = -58.6430628670095
x42 = 16.7551608191456
x43 = 29.3215314335047
x44 = 55.5014702134197
x45 = -57.5958653158129
x46 = -45.0294947014537
x47 = 17.8023583703422
x48 = -2.0943951023932
x49 = -38.7463093942741
x50 = -64.9262481741891
x51 = -51.3126800086333
x52 = -52.3598775598299
x53 = 42.9350995990605
x54 = 61.7846555205993
x55 = -5606.69568910658
x56 = -1.0471975511966
x57 = 99.4837673636768
x58 = -70.162235930172
x59 = 79.5870138909414
x60 = 48.1710873550435
x61 = -95.2949771588904
x62 = 93.2005820564972
x63 = 4.18879020478639
x64 = -101.57816246607
x65 = 11.5191730631626
x66 = -151.843644923507
x67 = 24.0855436775217
x68 = 86.9173967493176
x69 = 80.634211442138
x70 = -89.0117918517108
x71 = -39.7935069454707
x71 = -39.7935069454707
The graph