故(1/2 "," √3/2 "," √3)为所求点的直角坐标.

(2)∵(r,φ,θ)=(2"," π/4 "," 7π/4),

∴{■(x=rsinφcosθ=2sin π/4 cos 7π/4=1"," @y=rsinφsinθ=2sin π/4 sin 7π/4="-" 1"," @z=rcosφ=2cos π/4=√2 "." )┤

故(1,-1,√2)为所求点的直角坐标.

9已知点P的柱坐标为(√2 "," π/4 "," 5),点B的球坐标为(√6 "," π/3 "," π/6),求这两个点的直角坐标.

解设点P的直角坐标为(x,y,z),则x=√2 cos π/4=√2×√2/2=1,y=√2 sin π/4=1,z=5.

所以点P的直角坐标为(1,1,5).

设点B的直角坐标为(x1,y1,z1),

则x1=√6 sin π/3 cos π/6=√6×√3/2×√3/2=(3√6)/4,

y1=√6 sin π/3 sin π/6=√6×√3/2×1/2=(3√2)/4,

z1=√6 cos π/3=√6×1/2=√6/2.

所以点B的直角坐标为((3√6)/4 "," (3√2)/4 "," √6/2).

10结晶体的基本单位称为晶胞,食盐晶胞的示意图如图①所示("可看成是八个棱长为" 1/2 "的小正方体" ┤堆积成的正方体├ "　" /"　" ),图形中的点代表钠原子.如图②所示,建立空间直角坐标系O-xyz后,试写出下层钠原子所在位置的球坐标、柱坐标.

图①