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
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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
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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.