Parametric Representation in Spherical and Cartesian coordinates

[hughes]

Give a parametric representation of the following surfaces in terms of the given parameter variables:
a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi.
b)The graph of the function z = (x^3) - sqrt(y) in terms of the Cartesian variables x and y.

I'm not sure how to do these at all.
a) It's a sphere and theta ranges from 0 to pi/2. phi ranges from 0 to pi/2. Are the parametric equations just theta = t and phi = t, given that t ranges from 0 to pi/2? Or do we substitute x = psin(phi)cos(theta), etc. I'm really not sure what to do. Help.

 

[vela]

Give a parametric representation of the following surfaces in terms of the given parameter variables:
a) The first octant portion of the sphere (x^2) + (y^2) + (z^2) = 16 in terms of the spherical variables theta and phi.
b)The graph of the function z = (x^3) - sqrt(y) in terms of the Cartesian variables x and y.

I'm not sure how to do these at all.
a) It's a sphere and theta ranges from 0 to pi/2. phi ranges from 0 to pi/2. Are the parametric equations just theta = t and phi = t, given that t ranges from 0 to pi/2? Or do we substitute x = psin(phi)cos(theta), etc. I'm really not sure what to do. Help.

The surface is two-dimensional, so you need two parameters to describe it. The problem told you to use θ and Φ as your parameters. These parameters independently vary from 0 to π/2. Now you want to come up with some equation of the form r = f(θ,Φ).