Question

設角α的終邊為射線OP，射線OP₁與OP關于y軸對稱，射線OP₂與OP₁關于直線y＝-x對稱，則以OP₂為終邊的角的集合是．

1. A.
   {β|β＝k·360°+α，k∈Z}
2. B.
   {β|β＝(2k+1)·180°+α，k∈Z}
3. C.
   {β|β＝k·360°+90°+α，k∈Z}
4. D.
   {β|β＝k·360°+270°+α，k∈Z}

Answer 1

C
依題意射線OP₁所對應的角γ滿足α+γ＝k·360°+180°，從而射線OP₂所對應的角β＝α+γ-(90°-α)＝k·360°+180°-90°+α＝k·360°+90°+α．