四　柱坐标系与球坐标系简介

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基础巩固

1已知点P的柱坐标为(16"," π/3 "," 5),则其直角坐标为(　　)

A.(5,8,8√3)B.(8,8√3,5)

C.(8√3,8,5)D.(4,8√3,5)

解析设点P的直角坐标为(x,y,z).∵ρ=16,θ=π/3,z=5,∴x=ρcosθ=8,y=ρsinθ=8√3,z=5,

故点P的直角坐标是(8,8√3,5).

答案B

2已知点P的柱坐标为(2"," π/4 "," 3),若在空间直角坐标系中,点P在xOy平面上的射

影为Q,则点Q的柱坐标为0(　　)

A.(2,0,3)

B.(2"," π/4 "," 0)

C.(√2 "," π/4 "," 3)

D.(√2 "," π/4 "," 0)

答案B

3在球坐标系中,方程r=2(0≤φ≤π/2 "," 0≤θ<2π)表示(　　)

A.圆 B.半圆

C.球面 D.半球面

解析由空间点的球坐标的定义可知,

方程r=2(0≤φ≤π/2 "," 0≤θ<2π)表示半球面.

答案D

4已知点M的柱坐标为(4"," 7π/6 "," 1),则它的直角坐标为　　　　　.

解析设点M的直角坐标为(x,y,z).

∵ρ=4,θ=7π/6,z=1,

∴x=ρcosθ=4cos 7π/6=-2√3,