Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation 6*x^2+x-7=0
-
Equation (x^2-9)^2+(x^2+x-6)^2=0
-
Equation sin(2*x-pi/3)=0
-
Equation x/(75/5)=60
- Express {x} in terms of y where:
- 16*x+12*y=-13
- -1*x+5*y=15
- -8*x+8*y=-6
- -19*x-18*y=-6
- Integral of d{x}:
- sin(2*x-pi/3)
- Derivative of:
-
sin(2*x-pi/3)
-
Identical expressions
- sin(two *x-pi/ three)= zero
- sinus of (2 multiply by x minus Pi divide by 3) equally 0
- sinus of (two multiply by x minus Pi divide by three) equally zero
- sin(2x-pi/3)=0
- sin2x-pi/3=0
- sin(2*x-pi/3)=O
- sin(2*x-pi divide by 3)=0
-
Similar expressions
- sin(2*x+pi/3)=0
sin(2*x-pi/3)=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
/ pi\ sin|2*x - --| = 0 \ 3 /
$$\sin{\left(2 x - \frac{\pi}{3} \right)} = 0$$
Detail solution
Given the equation
$$\sin{\left(2 x - \frac{\pi}{3} \right)} = 0$$
- this is the simplest trigonometric equation
We get:
$$\sin{\left(2 x - \frac{\pi}{3} \right)} = 0$$
The equation is transformed to
$$\cos{\left(2 x + \frac{\pi}{6} \right)} = 0$$
This equation is transformed to
$$2 x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$2 x + \frac{\pi}{6} = \pi n + \frac{\pi}{2}$$
$$2 x + \frac{\pi}{6} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$2 x = \pi n + \frac{\pi}{3}$$
$$2 x = \pi n - \frac{2 \pi}{3}$$
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{3}$$
$$\sin{\left(2 x - \frac{\pi}{3} \right)} = 0$$
- this is the simplest trigonometric equation
with the change of sign in 0
We get:
$$\sin{\left(2 x - \frac{\pi}{3} \right)} = 0$$
Divide both parts of the equation by -1
The equation is transformed to
$$\cos{\left(2 x + \frac{\pi}{6} \right)} = 0$$
This equation is transformed to
$$2 x + \frac{\pi}{6} = \pi n + \operatorname{acos}{\left(0 \right)}$$
$$2 x + \frac{\pi}{6} = \pi n - \pi + \operatorname{acos}{\left(0 \right)}$$
Or
$$2 x + \frac{\pi}{6} = \pi n + \frac{\pi}{2}$$
$$2 x + \frac{\pi}{6} = \pi n - \frac{\pi}{2}$$
, where n - is a integer
Move
$$\frac{\pi}{6}$$
to right part of the equation
with the opposite sign, in total:
$$2 x = \pi n + \frac{\pi}{3}$$
$$2 x = \pi n - \frac{2 \pi}{3}$$
Divide both parts of the equation by
$$2$$
we get the answer:
$$x_{1} = \frac{\pi n}{2} + \frac{\pi}{6}$$
$$x_{2} = \frac{\pi n}{2} - \frac{\pi}{3}$$
Sum and product of roots
[src]
sum
pi 2*pi -- + ---- 6 3
$$\frac{\pi}{6} + \frac{2 \pi}{3}$$
=
5*pi ---- 6
$$\frac{5 \pi}{6}$$
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 = -63.8790506229925
x2 = 1228.88632632921
x3 = -79.5870138909414
x4 = -35.6047167406843
x5 = 88.4881930761125
x6 = -56.025068989018
x7 = 27.2271363311115
x8 = -34.0339204138894
x9 = -4.18879020478639
x10 = -40.317105721069
x11 = 38.2227106186758
x12 = -76.4454212373516
x13 = 90.0589894029074
x14 = 75.9218224617533
x15 = -85.870199198121
x16 = -73.3038285837618
x17 = 30.3687289847013
x18 = 55.5014702134197
x19 = -57.5958653158129
x20 = 33.5103216382911
x21 = 61.7846555205993
x22 = -92.1533845053006
x23 = -70.162235930172
x24 = 39.7935069454707
x25 = 24.0855436775217
x26 = 44.5058959258554
x27 = -21.4675497995303
x28 = -49.7418836818384
x29 = -87.4409955249159
x30 = 8.37758040957278
x31 = -100.007366139275
x32 = 68.0678408277789
x33 = 69.6386371545737
x34 = 9.94837673636768
x35 = -19.8967534727354
x36 = 17.8023583703422
x37 = 99.4837673636768
x38 = 14.6607657167524
x39 = 16.2315620435473
x40 = 46.0766922526503
x41 = -27.7507351067098
x42 = 66.497044500984
x43 = -84.2994028713261
x44 = 22.5147473507269
x45 = -13.6135681655558
x46 = 94.7713783832921
x47 = -43.4586983746588
x48 = -26.1799387799149
x49 = -62.3082542961976
x50 = 3.66519142918809
x51 = 74.3510261349584
x52 = 52.3598775598299
x53 = -78.0162175641465
x54 = -93.7241808320955
x55 = 77.4926187885482
x56 = 36.6519142918809
x57 = -51.3126800086333
x58 = 91.6297857297023
x59 = -16.7551608191456
x60 = -54.4542726622231
x61 = -5.75958653158129
x62 = 80.634211442138
x63 = -10.471975511966
x64 = -65.4498469497874
x65 = -32.4631240870945
x66 = -41.8879020478639
x67 = 2.0943951023932
x68 = -7.33038285837618
x69 = -71.733032256967
x70 = 47.6474885794452
x71 = -12.0427718387609
x72 = 82.2050077689329
x73 = 97.9129710368819
x74 = 96.342174710087
x75 = 31.9395253114962
x76 = 0.523598775598299
x77 = -98.4365698124802
x78 = -29.3215314335047
x79 = 53.9306738866248
x80 = 83.7758040957278
x81 = 58.6430628670095
x82 = 25.6563400043166
x83 = -95.2949771588904
x84 = 60.2138591938044
x85 = 11.5191730631626
x86 = -48.1710873550435
x87 = -18.3259571459405
x87 = -18.3259571459405
The graph