Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation (x+2)^2=(1-x)^2
-
Equation 2*cos(x)+1=0
-
Equation (-5*x-3)*(2*x-1)=0
-
Equation x^2-8x+15=0
- Express {x} in terms of y where:
- 7*x+13*y=-13
- 7*x+19*y=12
- 1*x+20*y=-17
- 14*x-16*y=-3
- Derivative of:
-
sin(2*x)
- Integral of d{x}:
-
sin(2*x)
- Graphing y =:
- sin(2*x)
-
Identical expressions
- sin(two *x)=-(sqrt(three)/ two)
- sinus of (2 multiply by x) equally minus ( square root of (3) divide by 2)
- sinus of (two multiply by x) equally minus ( square root of (three) divide by two)
- sin(2*x)=-(√(3)/2)
- sin(2x)=-(sqrt(3)/2)
- sin2x=-sqrt3/2
- sin(2*x)=-(sqrt(3) divide by 2)
-
Similar expressions
- sin(x)+sqrt((2-sqrt3)/2*(cos(x)+1))=0
- sin(2*x)=+(sqrt(3)/2)
- 3sin^2x+sinx-2=0
- cos(x)=-sqrt3/2
- sin(3*x+pi/4)=(-sqrt(3))/2
- sin^2(x)-cos^2(x)=1
- sin(x)+sqrt(((2-(sqrt(3)))/2)*(cos(x)+1))=0
sin(2*x)=-(sqrt(3)/2) equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___
-\/ 3
sin(2*x) = -------
2
$$\sin{\left(2 x \right)} = - \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(2 x \right)} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{3}$$
$$2 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
$$\sin{\left(2 x \right)} = - \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$2 x = 2 \pi n + \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)}$$
$$2 x = 2 \pi n - \operatorname{asin}{\left(- \frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$2 x = 2 \pi n - \frac{\pi}{3}$$
$$2 x = 2 \pi n + \frac{4 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \pi n - \frac{\pi}{6}$$
$$x_{2} = \pi n + \frac{2 \pi}{3}$$
Sum and product of roots
[src]
sum
pi 2*pi - -- + ---- 6 3
$$- \frac{\pi}{6} + \frac{2 \pi}{3}$$
=
pi -- 2
$$\frac{\pi}{2}$$
product
-pi 2*pi ----*---- 6 3
$$- \frac{\pi}{6} \frac{2 \pi}{3}$$
=
2 -pi ----- 9
$$- \frac{\pi^{2}}{9}$$
-pi^2/9
Rapid solution
[src]
-pi
x1 = ----
6
$$x_{1} = - \frac{\pi}{6}$$
2*pi
x2 = ----
3
$$x_{2} = \frac{2 \pi}{3}$$
x2 = 2*pi/3
Numerical answer
[src]
x1 = 90.0589894029074
x2 = 62.3082542961976
x3 = -1.0471975511966
x4 = -69.6386371545737
x5 = -73.3038285837618
x6 = 74.3510261349584
x7 = -31.9395253114962
x8 = -67.0206432765823
x9 = -85.870199198121
x10 = -261.799387799149
x11 = -29.3215314335047
x12 = 93.7241808320955
x13 = 64.9262481741891
x14 = 68.5914396033772
x15 = 18.3259571459405
x16 = -50.789081233035
x17 = -3.66519142918809
x18 = 20.943951023932
x19 = 80.634211442138
x20 = -95.2949771588904
x21 = -79.5870138909414
x22 = -242.426233102012
x23 = 49.7418836818384
x24 = -6.80678408277789
x25 = 46.0766922526503
x26 = -47.6474885794452
x27 = -72.7802298081635
x28 = 30.3687289847013
x29 = 100.007366139275
x30 = 87.4409955249159
x31 = -60.2138591938044
x32 = 27.7507351067098
x33 = 65.4498469497874
x34 = -16.2315620435473
x35 = -44.5058959258554
x36 = -28.7979326579064
x37 = -97.9129710368819
x38 = -23.0383461263252
x39 = 39900.3210956928
x40 = -41.8879020478639
x41 = -19.8967534727354
x42 = 14.6607657167524
x43 = 21.4675497995303
x44 = -66.497044500984
x45 = 15.1843644923507
x46 = 84.2994028713261
x47 = -75.9218224617533
x48 = -82.2050077689329
x49 = -53.9306738866248
x50 = 37.1755130674792
x51 = 58.6430628670095
x52 = -9.94837673636768
x53 = 71.2094334813686
x54 = -88.4881930761125
x55 = -13.6135681655558
x56 = 40.317105721069
x57 = 8.90117918517108
x58 = -91.6297857297023
x59 = 34.0339204138894
x60 = -38.2227106186758
x61 = 71.733032256967
x62 = -4.18879020478639
x63 = -7.33038285837618
x64 = -45.0294947014537
x65 = 12.0427718387609
x66 = 96.342174710087
x67 = 52.3598775598299
x68 = -25.6563400043166
x69 = -94.7713783832921
x70 = -89.0117918517108
x71 = 36.6519142918809
x72 = 5.75958653158129
x73 = -35.6047167406843
x74 = -16.7551608191456
x75 = 78.0162175641465
x76 = -51.3126800086333
x77 = 124.616508592395
x78 = -22.5147473507269
x79 = -57.5958653158129
x80 = 43.4586983746588
x81 = -0.523598775598299
x82 = 86.9173967493176
x83 = 24.0855436775217
x84 = -1257.16066021152
x85 = -60.7374579694027
x86 = 56.025068989018
x87 = 42.9350995990605
x88 = -63.8790506229925
x89 = 2.0943951023932
x90 = 68.0678408277789
x91 = 8.37758040957278
x91 = 8.37758040957278