若角a的终边与6pi/7角的终边相同,求在[0,2pi)内终边与a/3角的终边相同的角.

Question

若角a的终边与6pi/7角的终边相同,求在[0,2pi)内终边与a/3角的终边相同的角.

Answer 1

a的终边与6π/7角的终边相同
所以a=2kπ+6π/7
所以a/3=2kπ/3+2π/7
0<=2kπ/3+2π/7<=2π
0<=2k/3+2/7<=2
-2/7<=2k/3<=12/7
-3/7<=k<=18/7
k是整数
所以k=0,1,2
a/3=2kπ/3+2π/7
所以a/3=2π/7,20π/21,34π/21