Question

I have a calcua 3 questions, can any one help?

Answer 1

(1) The point P has Cartesian coordinates (√2, 1, 1). Find (a) the cylindrical coordi- nates of P ,
and (b) the spherical coordinates of P .

(2) Sketch the set of points in space satisfying the cylindrical coordinate conditions
π1 ≤ r ≤ 2, 0 ≤ θ ≤ , and 1 ≤ z ≤ 2.

(3) Use cylindrical coordinates to describe the line through the point (1, 1, 0) and par- allel to
the z-axis. (This is the reverse of problem 2 in the sense that you need to specify the conditions
r, θ, and z need to satisfy.)

(4) Sketch the set of points in space satisfying the spherical coordinate conditions ρ = 2,














π π














0 ≤ θ ≤ 2 , and 0 ≤ φ ≤ 4 .

(5) Use spherical coordinates to describe the region above the xy-plane between the spheres of
radius 1 and 3 centered at the origin. (This is the reverse of problem 4.)

(6) (Bonus question: worth 10 points. Total points for assignment not to exceed 100.) Determine
the Cartesian equation of the surface with spherical coordinate equa- tion ρ = 2 cos θ sin φ − 2
sin θ sin φ + 2 cos φ. It turns out this describes a sphere.
What is the center and radius of this sphere?
1

Answer 2

You'll have more luck getting help if you ask one at a time. No one will be willing to invest the time to address all of these questions at once.