Mister Exam
Other calculators
-
How to use it?
- Equation:
-
Equation sin6x=1/2
-
Equation sin((2*x+2*pi)/3)*cos((4*x+pi)/3)-cos(2*x)=sin(x)^2/cos(-(-pi)/3)
-
Equation tgx=-(3/4)
-
Equation 10/(x+7)=-5/8
- Express {x} in terms of y where:
- 15*x-15*y=16
- 9*x+18*y=6
- (x^2+y^2-1)^3+x^2*y^3=0
- -1*x-19*y=-10
- Graphing y =:
-
sin6x
- Integral of d{x}:
- sin6x
-
1/2
- Derivative of:
-
sin6x
-
1/2
- Sum of series:
-
1/2
-
Identical expressions
- sin6x= one / two
- sinus of 6x equally 1 divide by 2
- sinus of 6x equally one divide by two
- sin6x=1 divide by 2
-
Similar expressions
- sin(6*x)=9/8
- sin(6*x-pi/6)=1/2
- sin(6*x)+cos(6*x)*sqrt(3)=-2*cos(8*x)
sin6x=1/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
Given the equation
$$\sin{\left(6 x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$6 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$6 x = 2 \pi n + \frac{\pi}{6}$$
$$6 x = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$6$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{36}$$
$$x_{2} = \frac{\pi n}{3} + \frac{5 \pi}{36}$$
$$\sin{\left(6 x \right)} = \frac{1}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$6 x = 2 \pi n + \operatorname{asin}{\left(\frac{1}{2} \right)}$$
$$6 x = 2 \pi n - \operatorname{asin}{\left(\frac{1}{2} \right)} + \pi$$
Or
$$6 x = 2 \pi n + \frac{\pi}{6}$$
$$6 x = 2 \pi n + \frac{5 \pi}{6}$$
, where n - is a integer
Divide both parts of the equation by
$$6$$
we get the answer:
$$x_{1} = \frac{\pi n}{3} + \frac{\pi}{36}$$
$$x_{2} = \frac{\pi n}{3} + \frac{5 \pi}{36}$$
Rapid solution
[src]
pi
x_1 = --
36
$$x_{1} = \frac{\pi}{36}$$
5*pi
x_2 = ----
36
$$x_{2} = \frac{5 \pi}{36}$$
Sum and product of roots
[src]
sum
pi 5*pi -- + ---- 36 36
$$\left(\frac{\pi}{36}\right) + \left(\frac{5 \pi}{36}\right)$$
=
pi -- 6
$$\frac{\pi}{6}$$
product
pi 5*pi -- * ---- 36 36
$$\left(\frac{\pi}{36}\right) * \left(\frac{5 \pi}{36}\right)$$
=
2 5*pi ----- 1296
$$\frac{5 \pi^{2}}{1296}$$
Numerical answer
[src]
x1 = -63.7917841603927
x2 = 16.1442955809475
x3 = -76.0090889243531
x4 = -27.8380015693096
x5 = -5.846852994181
x6 = -34.1211868764891
x7 = -47.7347550420449
x8 = 38.1354441560761
x9 = 82.1177413063332
x10 = 391.04101890933
x11 = 75.4854901487547
x12 = -49.8291501444381
x13 = 22.0784150377283
x14 = 80.02334620394
x15 = -67.9805743651791
x16 = 66.0607121879854
x17 = -51.9235452468313
x18 = -7.9412480965742
x19 = -59.6029939556064
x20 = 60.1265927312047
x21 = 58.0321976288115
x22 = -17.7150919077424
x23 = 70.2495023927718
x24 = 19.9840199353351
x25 = 11.9555053761612
x26 = 77.9289511015468
x27 = -73.9146938219599
x28 = -32.0267917740959
x29 = -87.8773278379145
x30 = -69.7259036171735
x31 = 46.16395871525
x32 = -21.9038821125288
x33 = 24.1728101401215
x34 = 44.0695636128568
x35 = 33.9466539512897
x36 = -65.8861792627859
x37 = 62.9191195343956
x38 = -43.8950306876574
x39 = 6.3704517697793
x40 = 28.3616003449079
x41 = 55.9378025264183
x42 = -91.717052192302
x43 = -78.1034840267462
x44 = 2.18166156499291
x45 = -83.6885376331281
x46 = -3.75245789178781
x47 = 18.2386906833407
x48 = -71.8202987195667
x49 = 36.0410490536829
x50 = 88.0518607631139
x51 = -95.9058423970884
x52 = -45.9894257900506
x53 = 68.1551072903786
x54 = 26.2672052425147
x55 = 94.3350460702935
x56 = 90.1462558655071
x57 = -61.6973890579996
x58 = -37.6118453804778
x59 = 14.0499004785544
x60 = 0.0872664625997165
x61 = -100.094632601875
x62 = 48.2583538176432
x63 = -10.0356431989674
x64 = 62.2209878335978
x65 = 31.8522588488965
x66 = -12.1300383013606
x67 = -85.7829327355213
x68 = -29.9323966717028
x69 = 9.86111027376796
x70 = 41.9751685104636
x71 = 53.4943415736262
x72 = -41.8006355852642
x73 = -81.245076680336
x74 = -56.1123354516177
x75 = -23.998277214922
x76 = -93.8114472946952
x77 = 4.27605666738611
x78 = 84.2121364087264
x79 = 50.3527489200364
x80 = 40.2298392584693
x81 = -54.0179403492245
x82 = -25.7436064669164
x83 = -89.9717229403077
x84 = 99.9200996766754
x85 = 63.9663170855922
x86 = -39.706240482871
x87 = 72.343897495165
x88 = -19.8094870101356
x89 = -98.0002374994816
x90 = -15.6206968053492
x91 = 92.2406509679003
x92 = -2.00712863979348
x93 = 96.7785070230856
x93 = 96.7785070230856
The graph