答案C

5在极坐标系中,点A的极坐标是(3"," π/6),则

(1)点A关于极轴的对称点的极坐标是　　　　;

(2)点A关于极点的对称点的极坐标是　　　　;

(3)点A关于过极点且垂直于极轴的直线的对称点的极坐标是　　　　.(本题中规定ρ>0,θ∈[0,2π))

答案(1)(3"," 11π/6)　(2)(3"," 7π/6)　(3)(3"," 5π/6)

6已知点A(3"," 4π/3),则适合ρ>0,-π<θ≤π的点A的极坐标为　　　　　.

解析当ρ>0,-π<θ≤π时,根据 4π/3 与-2π/3 是终边相同的角,可得满足题意的点A的极坐标为(3",-" 2π/3).

答案(3",-" 2π/3)

7点M(6"," 5π/6)到极轴所在直线的距离为　　　　.

解析依题意知点M(6"," 5π/6)到极轴所在直线的距离为d=6×sin5π/6=3.

答案3

8已知在极坐标系中,极点为O,0≤θ<2π,M(3"," π/3),在直线OM上与点M距离为4的点的极坐标为　　　　　　　　.

解析

如图,|OM|=3,∠xOM=π/3.

在直线OM上取点P,Q,使|OP|=7,|OQ|=1.

显然有|PM|=|OP|-|OM|=7-3=4,|QM|=|OM|+|OQ|=3+1=4.

点P,Q都满足条件,且∠xOP=π/3,∠xOQ=4π/3.

故满足条件的点的极坐标为(7"," π/3),(1"," 4π/3).

答案(7"," π/3),(1"," 4π/3)