Graphing Coordinate Systems in R3: Spherical Equations and Inequalities

[STLCards002]

Homework Statement

Graph the surface in R³

Homework Equations

Spherical equation \rho = 2asin(\varphi)

The Attempt at a Solution

I think its just a sphere with a radius of 2
_______________________________________________

Homework Statement

Graph the solid whose given coordinates satisfy the inequalities

Homework Equations

a) 0 \leq r \leq 3, 0 \leq \theta \leq \pi/2, -1 \leq z \leq 2
b) 2r \leq z \leq 5 - 3r

The Attempt at a Solution

I figure these are cylinders because of variables used to describe the coordinates but besides that I'm having trouble know what to use the inequalities for
_______________________________________________

Homework Statement

Graph the solid whose given coordinates satisfy the inequalities

Homework Equations

a) 0 \leq \rho \leq 1, 0 \leq \theta \leq \pi/2,
b) 0 \leq \rho \leq 2/cos\varphi, 0 \leq \varphi \leq \pi/4

The Attempt at a Solution

Spheres, but same problem as with the others, I'm just not doing well at understanding how to use the inequalities to graph it

 

[tiny-tim]

Hi STLCards002!

Sorry, but everything is wrong.

The only thing I can suggest is that you draw a nice big diagram (take up a whole page), with x y and z axes marked, and just draw in the boundaries.

If it helps, pretend the inequalities are equalities … that will give you the boundaries, and you can work out which parts to shade, later.