It is known that a is the first quadrant angle (360K < a < 360K + 90), so why is k divided into odd and even when finding out which quadrant angle A / 2 is And what quadrant angle is a / 3? K = 3k, k = 3K + 1, k = 3K + 2. Why

It is known that a is the first quadrant angle (360K < a < 360K + 90), so why is k divided into odd and even when finding out which quadrant angle A / 2 is And what quadrant angle is a / 3? K = 3k, k = 3K + 1, k = 3K + 2. Why

180K ＜ A / 2 ＜ 180K + 45 when k is odd, a / 2 is in the third quadrant; when k is even, a / 2 is in the first quadrant; when k = 3T, 360t ＜ A / 3 ＜ 360t + 30, a / 3 is in the first quadrant; when k = 3T + 1, 360t + 120 ＜ A / 3 ＜ 360t + 150, a / 3 is in the second quadrant; when k = 3T + 2, 360t + 240 ＜ A /

The intersection of {x | x = 360K + 180, K belongs to Z} and {x | x = 360K, K belongs to Z}

{x | x = 360K + 180, K belongs to Z} → {x | x = 180 (2k + 1), K ∈ Z}
{x | x = 360K, K belongs to Z} → {x | x = 180.2k, K ∈ Z}
∴{x|x=180(2k+1),k∈z}∩{x|x=180·2k,k∈z}={x|x=180·n,k∈z}
^ ^

Let - 1480 ° be written in the form of α + 2K π (K ∈Ζ), where 0 ≤ α ≤ 2 π

320°+2kπ
When k = - 5