一道关羽极坐标方程的题目方程 r=sin(2θ-π/2) 表示一极坐标曲线,则极角θ的取值范围是:A [0,2π)B [π/4,9π/4]C [0,π/2] ∪ [π,3π/2]D [π/4,3π/4] ∪ [5π/4,7π/4]
问题描述:
一道关羽极坐标方程的题目
方程 r=sin(2θ-π/2) 表示一极坐标曲线,则极角θ的取值范围是:
A [0,2π)
B [π/4,9π/4]
C [0,π/2] ∪ [π,3π/2]
D [π/4,3π/4] ∪ [5π/4,7π/4]
答
r=sin(2θ-π/2)=-cos(2θ)≥0
∴cos(2θ)≤0
∴2θ∈[π/2,3π/2]∪ [5π/2, 7π/2]
∴θ∈[π/4, 3π/4] ∪ [5π/4, 7π/4]
选D