Mister Exam
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How to use it?
- Equation:
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Equation x^4=(3*x-4)^2
-
Equation 4-6*(x+2)=3-5*x
-
Equation 1/(x-3)^2-3/(x-3)-4=0
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Equation 1+sin(x)=0
- Express {x} in terms of y where:
- -11*x+15*y=7
- 6*x+17*y=3
- -17*x+1*y=-11
- 1*x+4*y=20
-
Identical expressions
- sin(3x+(pi/ thirteen))=sqrt3/ two
- sinus of (3x plus ( Pi divide by 13)) equally square root of 3 divide by 2
- sinus of (3x plus ( Pi divide by thirteen)) equally square root of 3 divide by two
- sin(3x+(pi/13))=√3/2
- sin3x+pi/13=sqrt3/2
- sin(3x+(pi divide by 13))=sqrt3 divide by 2
-
Similar expressions
- sin(x+pi*1/3)=sqrt(3)/2
- sin(3*x+pi/4)=(-sqrt(3))/2
- sin(3x-(pi/13))=sqrt3/2
- sin(x)*(2*sin(x)-1)-sqrt(3)*sin(x)+sqrt(3)/2=0
- sin(x)*cos(x)=(-sqrt(3))/((2*sin(x)))
sin(3x+(pi/13))=sqrt3/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ / pi\ \/ 3 sin|3*x + --| = ----- \ 13/ 2
$$\sin{\left(3 x + \frac{\pi}{13} \right)} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\sin{\left(3 x + \frac{\pi}{13} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x + \frac{\pi}{13} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$3 x + \frac{\pi}{13} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$3 x + \frac{\pi}{13} = 2 \pi n + \frac{\pi}{3}$$
$$3 x + \frac{\pi}{13} = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{13}$$
to right part of the equation
with the opposite sign, in total:
$$3 x = 2 \pi n + \frac{10 \pi}{39}$$
$$3 x = 2 \pi n + \frac{23 \pi}{39}$$
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} + \frac{10 \pi}{117}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{23 \pi}{117}$$
$$\sin{\left(3 x + \frac{\pi}{13} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$3 x + \frac{\pi}{13} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$3 x + \frac{\pi}{13} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$3 x + \frac{\pi}{13} = 2 \pi n + \frac{\pi}{3}$$
$$3 x + \frac{\pi}{13} = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Move
$$\frac{\pi}{13}$$
to right part of the equation
with the opposite sign, in total:
$$3 x = 2 \pi n + \frac{10 \pi}{39}$$
$$3 x = 2 \pi n + \frac{23 \pi}{39}$$
Divide both parts of the equation by
$$3$$
we get the answer:
$$x_{1} = \frac{2 \pi n}{3} + \frac{10 \pi}{117}$$
$$x_{2} = \frac{2 \pi n}{3} + \frac{23 \pi}{117}$$
Sum and product of roots
[src]
sum
10*pi 23*pi ----- + ----- 117 117
$$\frac{10 \pi}{117} + \frac{23 \pi}{117}$$
=
11*pi ----- 39
$$\frac{11 \pi}{39}$$
product
10*pi 23*pi -----*----- 117 117
$$\frac{10 \pi}{117} \frac{23 \pi}{117}$$
=
2 230*pi ------- 13689
$$\frac{230 \pi^{2}}{13689}$$
230*pi^2/13689
Rapid solution
[src]
10*pi
x1 = -----
117
$$x_{1} = \frac{10 \pi}{117}$$
23*pi
x2 = -----
117
$$x_{2} = \frac{23 \pi}{117}$$
x2 = 23*pi/117
Numerical answer
[src]
x1 = -51.7422995168165
x2 = 73.9214066267752
x3 = -85.6016870055065
x4 = -1.82588290977868
x5 = -958.964444703469
x6 = 17.0236730117601
x7 = 90.3275015955219
x8 = 29.9391094765181
x9 = -33.2418094456766
x10 = -14.043187673739
x11 = 11.0895535549794
x12 = -75.1297114935405
x13 = 98.7050820050947
x14 = -70.9409212887541
x15 = -47.902575162429
x16 = 94.5162918003083
x17 = -43.7137849576426
x18 = 21.5615290669453
x19 = 48.439599547658
x20 = -58.0254848239961
x21 = -60.1198799263893
x22 = -35.3362045480698
x23 = -7.7600023665594
x24 = 71.827011524382
x25 = -62.2142750287825
x26 = -22.4207680833118
x27 = -55.9310897216029
x28 = -64.3086701311757
x29 = 34.1278996813045
x30 = -81.4128968007201
x31 = 88.2331064931287
x32 = -20.3263729809186
x33 = 36.2222947836977
x34 = 13.1839486573726
x35 = 101.148542957887
x36 = 86.1387113907355
x37 = 46.3452044452648
x38 = -79.3185016983269
x39 = -6.01467311456507
x40 = 0.268512192614512
x41 = 52.6283897524444
x42 = -66.4030652335689
x43 = 8.6460926021873
x44 = -41.6193898552494
x45 = 80.2045919339548
x46 = 23.6559241693385
x47 = -3.92027801217188
x48 = 505.366797719774
x49 = -87.6960821078997
x50 = 25.7503192717317
x51 = -99.91338687186
x52 = 40.0620191380852
x53 = -83.5072919031133
x54 = 50.5339946500512
x55 = 76.0158017291684
x56 = -18.2319778785254
x57 = 65.5438262172024
x58 = 4.4573023974009
x59 = 96.6106869027015
x60 = -89.7904772102929
x61 = 84.0443162883423
x62 = 63.1003652644104
x63 = -31.1474143432834
x64 = -28.7039533904914
x65 = -37.430599650463
x66 = 27.8447143741249
x67 = -97.8189917694668
x68 = 54.7227848548376
x69 = -93.9792674150793
x70 = 6.5516974997941
x71 = 42.1564142404784
x72 = 69.7326164219888
x73 = -91.8848723126861
x74 = -68.4974603359621
x75 = -16.1375827761322
x76 = 92.4218966979151
x77 = 44.2508093428716
x78 = -116.668547691006
x79 = 10.7404877045805
x80 = 78.1101968315616
x81 = -11.9487925713458
x82 = -95.7245966670736
x83 = -9.8543974689526
x84 = -53.8366946192097
x85 = -45.8081800600358
x86 = -39.5249947528562
x87 = -49.9969702648222
x88 = 32.0335045789113
x89 = 2.36290729500771
x90 = 67.6382213195956
x91 = -76.8750407455349
x92 = 57.1662458076297
x93 = 19.1180681141533
x93 = 19.1180681141533