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cosx=√2/2 equation

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You have entered [src]

           ___
         \/ 2 
cos(x) = -----
           2

\cos{\left(x \right)} = \frac{\sqrt{2}}{2}

Simplify

Detail solution

Given the equation

\cos{\left(x \right)} = \frac{\sqrt{2}}{2}

- this is the simplest trigonometric equation
This equation is transformed to

x = \pi n + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}

x = \pi n - \pi + \operatorname{acos}{\left(\frac{\sqrt{2}}{2} \right)}

x = \pi n + \frac{\pi}{4}

x = \pi n - \frac{3 \pi}{4}

, where n - is a integer

The graph

Plot the graph f1(x)

Plot the graph f2(x)

Rapid solution [src]

     pi
x1 = --
     4

x_{1} = \frac{\pi}{4}

Simplify

     7*pi
x2 = ----
      4

x_{2} = \frac{7 \pi}{4}

Simplify

Sum and product of roots [src]

sum

    pi   7*pi
0 + -- + ----
    4     4

\left(0 + \frac{\pi}{4}\right) + \frac{7 \pi}{4}

2*pi

2 \pi

product

  pi 7*pi
1*--*----
  4   4

\frac{7 \pi}{4} \cdot 1 \frac{\pi}{4}

    2
7*pi 
-----
  16

\frac{7 \pi^{2}}{16}

7*pi^2/16

Numerical answer [src]

x1 = -13.3517687777566

x2 = 44.7676953136546

x3 = -7.06858347057703

x4 = 30.6305283725005

x5 = 87.1791961371168

x6 = -82.4668071567321

x7 = 63.6172512351933

x8 = -18.0641577581413

x9 = -19.6349540849362

x10 = -101.316363078271

x11 = 7.06858347057703

x12 = -38.484510006475

x13 = -76.1836218495525

x14 = -95.0331777710912

x15 = 57.3340659280137

x16 = -51.0508806208341

x17 = 99.7455667514759

x18 = 32.2013246992954

x19 = 80.8960108299372

x20 = -11.7809724509617

x21 = -32.2013246992954

x22 = 0.785398163397448

x23 = 76.1836218495525

x24 = 74.6128255227576

x25 = 51.0508806208341

x26 = -69.9004365423729

x27 = 5.49778714378214

x28 = 62.0464549083984

x29 = -63.6172512351933

x30 = -36.9137136796801

x31 = 68.329640215578

x32 = -0.785398163397448

x33 = 55.7632696012188

x34 = 93.4623814442964

x35 = -55.7632696012188

x36 = -25.9181393921158

x37 = -88.7499924639117

x38 = 88.7499924639117

x39 = 36.9137136796801

x40 = 25.9181393921158

x41 = -87.1791961371168

x42 = -30.6305283725005

x43 = 13.3517687777566

x44 = 49.4800842940392

x45 = 82.4668071567321

x46 = -44.7676953136546

x47 = 69.9004365423729

x48 = 95.0331777710912

x49 = -49.4800842940392

x50 = -74.6128255227576

x51 = 18.0641577581413

x52 = 38.484510006475

x53 = -351.072979038659

x54 = -68.329640215578

x55 = -182.997772071605

x56 = -80.8960108299372

x57 = 11.7809724509617

x58 = -5.49778714378214

x59 = -93.4623814442964

x60 = -162.577419823272

x61 = -99.7455667514759

x62 = -43.1968989868597

x63 = 19.6349540849362

x64 = -24.3473430653209

x65 = 24.3473430653209

x66 = -57.3340659280137

x67 = 43.1968989868597

x68 = -62.0464549083984

x68 = -62.0464549083984

The graph