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cos(x)=4/7

cos(x)=4/7 equation

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Numerical solution:

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The solution

You have entered [src] 
cos(x) = 4/7
cos⁡(x)=47\cos{\left(x \right)} = \frac{4}{7}
Simplify
Detail solution
Given the equation
cos⁡(x)=47\cos{\left(x \right)} = \frac{4}{7}
- this is the simplest trigonometric equation
This equation is transformed to
x=πn+acos⁡(47)x = \pi n + \operatorname{acos}{\left(\frac{4}{7} \right)}
x=πn−π+acos⁡(47)x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{7} \right)}
Or
x=πn+acos⁡(47)x = \pi n + \operatorname{acos}{\left(\frac{4}{7} \right)}
x=πn−π+acos⁡(47)x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{7} \right)}
, where n - is a integer
The graph
0-80-60-40-2020406080-1001002-2
Plot the graph f1(x)
Plot the graph f2(x)
Sum and product of roots [src] 
sum
0 + -acos(4/7) + 2*pi + acos(4/7)
acos⁡(47)+(0+(−acos⁡(47)+2π))\operatorname{acos}{\left(\frac{4}{7} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi\right)\right) 
=
2*pi
2π2 \pi 
product
1*(-acos(4/7) + 2*pi)*acos(4/7)
1(−acos⁡(47)+2π)acos⁡(47)1 \left(- \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{7} \right)} 
=
(-acos(4/7) + 2*pi)*acos(4/7)
(−acos⁡(47)+2π)acos⁡(47)\left(- \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{7} \right)} 
(-acos(4/7) + 2*pi)*acos(4/7)
Rapid solution [src] 
x1 = -acos(4/7) + 2*pi
x1=−acos⁡(47)+2πx_{1} = - \operatorname{acos}{\left(\frac{4}{7} \right)} + 2 \pi
Simplify 
x2 = acos(4/7)
x2=acos⁡(47)x_{2} = \operatorname{acos}{\left(\frac{4}{7} \right)}
Simplify
Numerical answer [src] 
x1 = 99.5684141669887
x2 = 57.511218512501
x3 = -43.0197464023724
x4 = -61.8693023239112
x5 = -99.5684141669887
x6 = -0.962550747884687
x7 = -26.095291976603
x8 = 19.8121066694234
x9 = 76.3607744340397
x10 = 63.7944038196806
x11 = 24.1701904808337
x12 = -87.0020435526295
x13 = -38.6616625909622
x14 = 51.2280332053214
x15 = 32.3784772837826
x16 = 70.0775891268601
x17 = -44.9448478981418
x18 = -88.9271450483989
x19 = 13.5289213622439
x20 = 30.4533757880132
x21 = -17.8870051736541
x22 = -57.511218512501
x23 = -74.4356729382704
x24 = 11.6038198664745
x25 = 36.7365610951928
x26 = -95.2103303555785
x27 = 26.095291976603
x28 = 38.6616625909622
x29 = -68.1524876310908
x30 = 87.0020435526295
x31 = 55.5861170167316
x32 = -24.1701904808337
x33 = -30.4533757880132
x34 = 95.2103303555785
x35 = 93.2852288598091
x36 = 88.9271450483989
x37 = -13.5289213622439
x38 = -93.2852288598091
x39 = 44.9448478981418
x40 = -101.493515662758
x41 = -76.3607744340397
x42 = -49.302931709552
x43 = -36.7365610951928
x44 = -5.3206345592949
x45 = -82.6439597412193
x46 = 5.3206345592949
x47 = -19.8121066694234
x48 = -11.6038198664745
x49 = -63.7944038196806
x50 = 49.302931709552
x51 = 82.6439597412193
x52 = 43.0197464023724
x53 = 0.962550747884687
x54 = 68.1524876310908
x55 = 17.8870051736541
x56 = -70.0775891268601
x57 = 74.4356729382704
x58 = -51.2280332053214
x59 = 61.8693023239112
x60 = -32.3784772837826
x61 = 7.24573605506427
x62 = -80.7188582454499
x63 = -55.5861170167316
x64 = -7.24573605506427
x65 = 80.7188582454499
x65 = 80.7188582454499
The graph
cos(x)=4/7 equation
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