Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation x/4+x=-5
-
Equation x^4-10x^2+9=0
-
Equation x-11=-7
-
Equation 7-4(3x-1)=5(1-2x)
- Express {x} in terms of y where:
- 8*x+1*y=4
- 19*x+2*y=17
- 11*x-9*y=-4
- 9*x+8*y=-4
- Limit of the function:
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sqrt(3)/2
- Derivative of:
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sqrt(3)/2
-
Identical expressions
- cos(pi/ two - three x/ two)=sqrt(3)/ two
- co sinus of e of ( Pi divide by 2 minus 3x divide by 2) equally square root of (3) divide by 2
- co sinus of e of ( Pi divide by two minus three x divide by two) equally square root of (3) divide by two
- cos(pi/2-3x/2)=√(3)/2
- cospi/2-3x/2=sqrt3/2
- cos(pi divide by 2-3x divide by 2)=sqrt(3) divide by 2
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Similar expressions
- cos(p/3+x)=(-sqrt(3))/2
- cos(pi/2+3x/2)=sqrt(3)/2
cos(pi/2-3x/2)=sqrt(3)/2 equation
The teacher will be very surprised to see your correct solution 😉
The solution
You have entered
[src]
___ /pi 3*x\ \/ 3 cos|-- - ---| = ----- \2 2 / 2
$$\cos{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)} = \frac{\sqrt{3}}{2}$$
Detail solution
Given the equation
$$\cos{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{3 x}{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{3 x}{2} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$\frac{3 x}{2} = 2 \pi n + \frac{\pi}{3}$$
$$\frac{3 x}{2} = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{3}{2}$$
we get the answer:
$$x_{1} = \frac{4 \pi n}{3} + \frac{2 \pi}{9}$$
$$x_{2} = \frac{4 \pi n}{3} + \frac{4 \pi}{9}$$
$$\cos{\left(- \frac{3 x}{2} + \frac{\pi}{2} \right)} = \frac{\sqrt{3}}{2}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$\frac{3 x}{2} = 2 \pi n + \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)}$$
$$\frac{3 x}{2} = 2 \pi n - \operatorname{asin}{\left(\frac{\sqrt{3}}{2} \right)} + \pi$$
Or
$$\frac{3 x}{2} = 2 \pi n + \frac{\pi}{3}$$
$$\frac{3 x}{2} = 2 \pi n + \frac{2 \pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$\frac{3}{2}$$
we get the answer:
$$x_{1} = \frac{4 \pi n}{3} + \frac{2 \pi}{9}$$
$$x_{2} = \frac{4 \pi n}{3} + \frac{4 \pi}{9}$$
Rapid solution
[src]
2*pi
x1 = ----
9
$$x_{1} = \frac{2 \pi}{9}$$
4*pi
x2 = ----
9
$$x_{2} = \frac{4 \pi}{9}$$
x2 = 4*pi/9
Sum and product of roots
[src]
sum
2*pi 4*pi ---- + ---- 9 9
$$\frac{2 \pi}{9} + \frac{4 \pi}{9}$$
=
2*pi ---- 3
$$\frac{2 \pi}{3}$$
product
2*pi 4*pi ----*---- 9 9
$$\frac{2 \pi}{9} \frac{4 \pi}{9}$$
=
2 8*pi ----- 81
$$\frac{8 \pi^{2}}{81}$$
8*pi^2/81
Numerical answer
[src]
x1 = -90.7571211037051
x2 = -86.5683308989187
x3 = -37.0009801422798
x4 = 60.0393262686049
x5 = -16.0570291183478
x6 = -87.2664625997165
x7 = -78.190750489346
x8 = -28.623399732707
x9 = 38.3972435438752
x10 = 76.0963553869528
x11 = 18.151424220741
x12 = 47.4729556542458
x13 = -62.1337213709981
x14 = -74.0019602845596
x15 = 4.88692190558412
x16 = 42.5860337486616
x17 = -91.4552528045029
x18 = 9.07571211037051
x19 = 80.2851455917392
x20 = 9.77384381116824
x21 = -99.8328332140756
x22 = -48.8692190558412
x23 = -19.5476876223365
x24 = -69.8131700797732
x25 = -78.8888821901437
x26 = 5.58505360638185
x27 = 13.2645023151569
x28 = 93.5496479068961
x29 = 85.1720674973233
x30 = 772.133661082291
x31 = 13.9626340159546
x32 = -65.6243798749868
x33 = -27.9252680319093
x34 = 50.9636141582344
x35 = -82.3795406941324
x36 = -1976.41084495838
x37 = 17.4532925199433
x38 = 89.3608577021097
x39 = -41.1897703470662
x40 = 80.9832772925369
x41 = 68.4169066781777
x42 = 55.1524043630208
x43 = -49.567350756639
x44 = 612.959633300409
x45 = -95.6440430092893
x46 = -7.67944870877505
x47 = -83.0776723949301
x48 = 97.7384381116825
x49 = -32.8121899374934
x50 = 1.39626340159546
x51 = -23.7364778271229
x52 = 55.8505360638185
x53 = -2.79252680319093
x54 = 25.8308729295161
x55 = 30.0196631343025
x56 = -6.98131700797732
x57 = 39.095375244673
x58 = -53.7561409614254
x59 = -53.0580092606276
x60 = 22.3402144255274
x61 = -40.4916386462684
x62 = -57.9449311662117
x63 = 43.2841654494594
x64 = -11.8682389135614
x65 = 34.2084533390889
x66 = 97.0403064108847
x67 = -74.7000919853573
x68 = 691.848515490552
x69 = -99.1347015132779
x70 = 46.774823953448
x71 = -45.3785605518526
x72 = 101.229096615671
x73 = -44.6804288510548
x74 = 21.6420827247297
x75 = -3.49065850398866
x76 = 0.698131700797732
x77 = -94.9459113084915
x78 = 71.9075651821664
x79 = 34.9065850398866
x80 = 84.4739357965256
x81 = -36.3028484414821
x82 = 92.8515162060983
x83 = 59.3411945678072
x84 = 51.6617458590322
x85 = -32.1140582366957
x86 = 88.6627260013119
x87 = 64.2281164733913
x87 = 64.2281164733913