Let a = {α | α = 2K π + π / 3, K ∈ Z} be the set of angles α Finding all angles of interval [- 4 π, 4 π] in set a

Let a = {α | α = 2K π + π / 3, K ∈ Z} be the set of angles α Finding all angles of interval [- 4 π, 4 π] in set a

-11π/3,-7π/3,π/3,7π/3

On a mathematical problem of set, we know that a = {x | x = 2K + 1, K belongs to Z}. Why can we say that a = {1,3,5,7,9} can be obtained?
I understand,

Wrong
A = {x | x = 2K + 1, K ∈ Z} indicates that the element of a is odd
And you are listed below are positive odd numbers, negative how not
So we should write a = {..., - 3, - 1,1,3,5,7,...}
A = {± 1, ± 3, ± 5, ± 7,...}
If you don't understand, please hi me, I wish you a happy study!

It is known that the equation 2Sin ^ 2x + 6cos ^ 2x = 5-2k about X has a solution, and K ∈ Z, find the value of K

2sin^2x+6cos^2x=5-2k
2+4cos^2x=5-2k
4cos^2x=3-2k
4cos^2x-2=3-2k-2
2(2cos^2x-1)=1-2k
2cos2x=1-2k
cos2x=(1-2k)/2
-1