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cos2x-1=0

cos2x-1=0 equation

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Numerical solution:

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The solution

You have entered [src]
cos(2*x) - 1 = 0
cos(2x)1=0\cos{\left(2 x \right)} - 1 = 0
Detail solution
Given the equation
cos(2x)1=0\cos{\left(2 x \right)} - 1 = 0
- this is the simplest trigonometric equation
Move -1 to right part of the equation

with the change of sign in -1

We get:
cos(2x)1+1=1\cos{\left(2 x \right)} - 1 + 1 = 1
This equation is transformed to
2x=πn+acos(1)2 x = \pi n + \operatorname{acos}{\left(1 \right)}
2x=πnπ+acos(1)2 x = \pi n - \pi + \operatorname{acos}{\left(1 \right)}
Or
2x=πn2 x = \pi n
2x=πnπ2 x = \pi n - \pi
, where n - is a integer
Divide both parts of the equation by
22
we get the answer:
x1=πn2x_{1} = \frac{\pi n}{2}
x2=πn2π2x_{2} = \frac{\pi n}{2} - \frac{\pi}{2}
The graph
0-80-60-40-2020406080-1001002-4
Sum and product of roots [src]
sum
0 + 0 + pi
(0+0)+π\left(0 + 0\right) + \pi
=
pi
π\pi
product
1*0*pi
10π1 \cdot 0 \pi
=
0
00
0
Rapid solution [src]
x1 = 0
x1=0x_{1} = 0
x2 = pi
x2=πx_{2} = \pi
Numerical answer [src]
x1 = 6.28318528425126
x2 = -40.8407042660168
x3 = 21.9911485851964
x4 = 69.1150385885879
x5 = 47.123890018392
x6 = -1734.15914475848
x7 = 75.3982239388525
x8 = 56.5486676091327
x9 = -40.8407046898283
x10 = 81.6814091761104
x11 = -31.4159267959754
x12 = -65.9734457650176
x13 = 3.14159244884412
x14 = 69.1150381602162
x15 = -91.106187201329
x16 = 47.123889589354
x17 = -91.1061872003049
x18 = -69.1150386737158
x19 = -3.14159311568248
x20 = 31.4159267865366
x21 = -59.6902604576401
x22 = -84.8230018263493
x23 = -47.1238900492539
x24 = 0.0
x25 = 91.1061867314459
x26 = -106.814150357553
x27 = 62.8318524523063
x28 = 9.42477859080277
x29 = -84.82300141007
x30 = 100.530964766599
x31 = -69.1150386253436
x32 = -21.9911485864515
x33 = 25.1327414478072
x34 = -6371388.6625218
x35 = -18.8495556944209
x36 = 97.3893727097471
x37 = -9.42477812668337
x38 = 9.42477821024198
x39 = 25.1327410188866
x40 = -34.5575189701076
x41 = -97.3893724403711
x42 = -62.8318528379059
x43 = 62.8318528326557
x44 = 12.5663704518704
x45 = -15.7079632965264
x46 = -87.9645943587732
x47 = -50.2654822953391
x48 = 34.5575190304759
x49 = 65.9734457528975
x50 = 75.3982241944528
x51 = 37.6991120192083
x52 = 40.8407042560881
x53 = -53.4070752836338
x54 = 28.2743338652012
x55 = -72.2566308741333
x56 = 78.5398161878405
x57 = -3.14159289677385
x58 = -12.5663703661411
x59 = 91.1061871583643
x60 = 40.840703919946
x61 = -81.6814090380061
x62 = -62.8318532583801
x63 = -31.4159267051849
x64 = -78.5398160958028
x65 = -18.8495561207399
x66 = 18.8495556796107
x67 = -12.5663700417108
x68 = -34.5575189426108
x69 = 84.8230010166547
x70 = -75.3982238620294
x71 = 87.9645943357576
x72 = 31.4159271479423
x73 = -25.132741632083
x74 = -43.9822971745789
x75 = -37.6991118771514
x76 = 43.982297169427
x77 = -47.123890151099
x78 = -25.132741473063
x79 = 59.6902605976901
x80 = -28.2743337166085
x81 = 53.4070753627408
x82 = 15.7079634406648
x83 = 53.4070756765307
x84 = -56.5486675191652
x85 = 94.2477796093525
x86 = -100.530964672522
x87 = 97.3893725148693
x88 = -6.28318513794069
x89 = 84.8230014093114
x90 = -94.2477794529919
x91 = 3.14159287686128
x92 = 18.8495554002244
x93 = 72.256631027719
x94 = 50.2654824463473
x94 = 50.2654824463473
The graph
cos2x-1=0 equation