082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

174 Chapter 4 Coordinate systems
7 Apoint has Cartesian coordinates (−1,−1,2).
Calculate the sphericalpolar coordinatesofthe point.
8 Describe the surfaceR = 2,0 ◦ θ 180 ◦ ,
0 ◦ φ 180 ◦ .
9 Describe the three-dimensional surface defined
byx=y.
10 Thespheredefined byR = 2 intersects the plane
defined byz = 1. Describethe curve ofintersection.
Solutions
1 7
2 5, 216.87 ◦
3 −2.5, −4.3301
4 FigureS.10 illustratesthe surface.
y
5 (4.1231,104.04 ◦ ,1)
6 y--z plane
7 R = √ 6, θ = 225 ◦ , φ = 35.26 ◦
8 Ahemisphereofradius2.Theflat surfaceison the
x--z plane.
9 Thesurfaceis aplanegenerated bymoving the line
y =xup anddown thezaxis.
10 Acircle ofradius √ 3,centre (0,0,1),in the plane
z=1.
O 1 4
FigureS.10
x