若θ角的终边与8π/5的终边相同,则在0,2π内终边与θ/4角的终边相同的角

Question

若θ角的终边与8π/5的终边相同,则在【0,2π】内终边与θ/4角的终边相同的角

Answer 1

若角α的终边与8π/5的终边相同,则在[0,2π]上终边与α/4的终边相同的角是
设α= 2kπ+8π/5 ,则α/4 = kπ/2 + 2π/5
所以 k=0时,α/4 = 2π/5
k=1时,α/4 = π/2 + 2π/5 = 9π/10
k=2时,α/4 = π + 2π/5 = 7π/5
k=3时,α/4 = 3π/2 + 2π/5 =19π/10