Cos 5x = корень 2 / 2

Solve cos(5x) = √2/2.

• For cos θ = √2/2, the general solution is θ = 2πn ± π/4, n ∈ Z.
• Let θ = 5x. Then 5x = 2πn ± π/4.

Thus the solutions are

• x = (2πn ± π/4)/5 = (2πn)/5 ± π/20, n ∈ Z.

If you want solutions in [0, 2π), you get two families with n from 0 to 4:

• x = π/20 + (2πn)/5
• x = -π/20 + (2πn)/5

For n = 0..4, this yields: π/20, 7π/20, 9π/20, 3π/4, 17π/20, 23π/20, 5π/4, 31π/20, 33π/20, 39π/20.