Mister Exam
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How to use it?
- Equation:
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Equation 3x²-27=0
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Equation sin5x-sqrt(3)cos5x=0
- Equation sin*2x-4sinxcosx+cos*2x=0
- Express {x} in terms of y where:
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Identical expressions
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-
Similar expressions
- sin5x+sqrt(3)cos5x=0
sin5x-sqrt(3)cos5x=0 equation
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The solution
You have entered
[src]
___ sin(5*x) - \/ 3 *cos(5*x) = 0
$$\sin{\left(5 x \right)} - \sqrt{3} \cos{\left(5 x \right)} = 0$$
Detail solution
Given the equation
$$\sin{\left(5 x \right)} - \sqrt{3} \cos{\left(5 x \right)} = 0$$
transform:
$$\frac{\sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} = \sqrt{3}$$
or
$$\tan{\left(5 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Or
$$5 x = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{\pi n}{5} - \frac{\pi}{15}$$
$$\sin{\left(5 x \right)} - \sqrt{3} \cos{\left(5 x \right)} = 0$$
transform:
$$\frac{\sin{\left(5 x \right)}}{\cos{\left(5 x \right)}} = \sqrt{3}$$
or
$$\tan{\left(5 x \right)} = \sqrt{3}$$
- this is the simplest trigonometric equation
This equation is transformed to
$$5 x = \pi n + \operatorname{atan}{\left(- \sqrt{3} \right)}$$
Or
$$5 x = \pi n - \frac{\pi}{3}$$
, where n - is a integer
Divide both parts of the equation by
$$5$$
we get the answer:
$$x_{1} = \frac{\pi n}{5} - \frac{\pi}{15}$$
Sum and product of roots
[src]
sum
pi -- 15
$$\left(\frac{\pi}{15}\right)$$
=
pi -- 15
$$\frac{\pi}{15}$$
product
pi -- 15
$$\left(\frac{\pi}{15}\right)$$
=
pi -- 15
$$\frac{\pi}{15}$$
Numerical answer
[src]
x1 = -87.7551547902749
x2 = 37.9085513533168
x3 = -9.84365698124802
x4 = 66.182885235625
x5 = 22.2005880853679
x6 = 98.2271303022409
x7 = -33.7197611485304
x8 = 59.8996999284454
x9 = 46.0766922526503
x10 = 68.0678408277789
x11 = -95.9232956896084
x12 = 8.37758040957278
x13 = 32.2536845768552
x14 = 15.9174027781883
x15 = -43.7728576400178
x16 = -51.9409985393512
x17 = 20.315632493214
x18 = -23.6666646570431
x19 = 54.2448331519838
x20 = 34.1386401690091
x21 = 49.2182849062401
x22 = 100.112085894395
x23 = 74.3510261349584
x24 = -7.95870138909414
x25 = -97.8082512817622
x26 = -40.00294645571
x27 = 86.2890782185997
x28 = 0.20943951023932
x29 = 5.86430628670095
x30 = 64.2979296434711
x31 = 52.3598775598299
x32 = -21.7817090648892
x33 = 93.8289005872152
x34 = 14.0324471860344
x35 = -6.07374579694027
x36 = 85.6607596878817
x37 = 69.9527964199327
x38 = -89.6401103824288
x39 = -45.6578132321717
x40 = -79.5870138909414
x41 = -50.0560429471974
x42 = 24.0855436775217
x43 = 59.2713813977274
x44 = 76.2359817271123
x45 = -13.6135681655558
x46 = -1026.46303968291
x47 = -11.7286125734019
x48 = 10.2625360017267
x49 = -104.71975511966
x50 = -8353.91374491574
x51 = -85.870199198121
x52 = 3.97935069454707
x53 = -1.67551608191456
x54 = -31.8348055563766
x55 = -99.6932068739161
x56 = 79.3775743807021
x57 = 88.1740338107535
x58 = 91.9439449950613
x59 = 47.9616478448042
x60 = 96.342174710087
x61 = 56.1297887441376
x62 = 78.1209373192662
x63 = -67.6489618073002
x64 = -28.0648943720688
x65 = 25.9704992696756
x66 = 80.0058929114201
x67 = 44.1917366604964
x68 = -48.1710873550435
x69 = 58.0147443362915
x70 = 42.3067810683426
x71 = -16.1268422884276
x72 = 36.023595761163
x73 = -65.7640062151463
x74 = -38.1179908635562
x75 = -92.7817030360186
x76 = -63.8790506229925
x77 = -41.8879020478639
x78 = 12.1474915938805
x79 = -83.9852436059671
x80 = -72.0471915223259
x81 = 30.3687289847013
x82 = 2.0943951023932
x83 = -75.8171027066337
x84 = -94.0383400974545
x85 = 81.8908485035739
x86 = -60.1091394386847
x87 = -53.8259541315051
x88 = -56.339228254377
x89 = -29.9498499642227
x90 = -77.7020582987875
x91 = -19.8967534727354
x92 = -61.9940950308386
x93 = -35.6047167406843
x94 = -18.0117978805815
x95 = 90.0589894029074
x96 = -73.9321471144798
x97 = -82.1002880138133
x98 = -55.710909723659
x98 = -55.710909723659
The graph