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cos(x)=(4/5)

cos(x)=(4/5) equation

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Numerical solution:

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The solution

You have entered [src] 
cos(x) = 4/5
cos⁡(x)=45\cos{\left(x \right)} = \frac{4}{5}
Simplify
Detail solution
Given the equation
cos⁡(x)=45\cos{\left(x \right)} = \frac{4}{5}
- this is the simplest trigonometric equation
This equation is transformed to
x=πn+acos⁡(45)x = \pi n + \operatorname{acos}{\left(\frac{4}{5} \right)}
x=πn−π+acos⁡(45)x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{5} \right)}
Or
x=πn+acos⁡(45)x = \pi n + \operatorname{acos}{\left(\frac{4}{5} \right)}
x=πn−π+acos⁡(45)x = \pi n - \pi + \operatorname{acos}{\left(\frac{4}{5} \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(4/5) + 2*pi + acos(4/5)
acos⁡(45)+(0+(−acos⁡(45)+2π))\operatorname{acos}{\left(\frac{4}{5} \right)} + \left(0 + \left(- \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi\right)\right) 
=
2*pi
2π2 \pi 
product
1*(-acos(4/5) + 2*pi)*acos(4/5)
1(−acos⁡(45)+2π)acos⁡(45)1 \left(- \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{5} \right)} 
=
(-acos(4/5) + 2*pi)*acos(4/5)
(−acos⁡(45)+2π)acos⁡(45)\left(- \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi\right) \operatorname{acos}{\left(\frac{4}{5} \right)} 
(-acos(4/5) + 2*pi)*acos(4/5)
Rapid solution [src] 
x1 = -acos(4/5) + 2*pi
x1=−acos⁡(45)+2πx_{1} = - \operatorname{acos}{\left(\frac{4}{5} \right)} + 2 \pi
Simplify 
x2 = acos(4/5)
x2=acos⁡(45)x_{2} = \operatorname{acos}{\left(\frac{4}{5} \right)}
Simplify
Numerical answer [src] 
x1 = 99.8874638060801
x2 = -87.3210931917209
x3 = -37.0556107342842
x4 = 87.3210931917209
x5 = 37.0556107342842
x6 = 30.7724254271046
x7 = -12486222.9460819
x8 = 94.8912807164871
x9 = 44.6257982590504
x10 = 5.6396841983863
x11 = -81.0379078845413
x12 = -25.7762423375116
x13 = 57.1921688734096
x14 = -24.4892401199251
x15 = -18.2060548127455
x16 = -63.4753541805892
x17 = 76.0417247949483
x18 = -55.905166655823
x19 = -49.6219813486434
x20 = -0.643501108793284
x21 = 93.6042784989005
x22 = -13.2098717231525
x23 = 74.7547225773617
x24 = -101.174466023667
x25 = -99.8874638060801
x26 = 6.92668641597287
x27 = 81.0379078845413
x28 = 49.6219813486434
x29 = -5.6396841983863
x30 = 68.4715372701822
x31 = 43.3387960414638
x32 = -94.8912807164871
x33 = 13.2098717231525
x34 = -38.3426129518708
x35 = 55.905166655823
x36 = -69.7585394877687
x37 = -93.6042784989005
x38 = -88.6080954093075
x39 = 0.643501108793284
x40 = -57.1921688734096
x41 = 3550.64319966526
x42 = 38.3426129518708
x43 = -74.7547225773617
x44 = -43.3387960414638
x45 = -32.0594276446912
x46 = -11.9228695055659
x47 = 88.6080954093075
x48 = 11.9228695055659
x49 = 18.2060548127455
x50 = -6.92668641597287
x51 = 82.3249101021279
x52 = -82.3249101021279
x53 = 63.4753541805892
x54 = -19.493057030332
x55 = -44.6257982590504
x56 = -3210.06419085998
x57 = -76.0417247949483
x58 = -30.7724254271046
x59 = 62.1883519630026
x60 = 25.7762423375116
x61 = 32.0594276446912
x62 = 69.7585394877687
x63 = -68.4715372701822
x64 = 19.493057030332
x65 = -50.90898356623
x66 = 50.90898356623
x67 = -62.1883519630026
x68 = 24.4892401199251
x68 = 24.4892401199251
The graph
cos(x)=(4/5) equation
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