Cylindrical and Cartesian Coord. dot product

[Cmwarre]

Homework Statement

I'm given 2 unit vectors a_x and a_theta.
I need to find the dot product between the two.

Homework Equations

Conversion from Cylindrical to Cartesian

x = r * sin(theta)
y = r * cos(theta)
z = z

Conversion from Cartesian to Cylindrical

r = sqrt(x^2 + y^2)
theta = tan^-1(x/y)
z = z

The Attempt at a Solution

I'm just curious if you were my teacher what kind of answer would you want?
I think the point he's trying to prove is that theta is the angle between the x and y plane but I have no idea how to put that mathematically with the given formulas..

 

[vela]

Homework Statement

I'm given 2 unit vectors a_x and a_theta.
I need to find the dot product between the two.

Homework Equations

Conversion from Cylindrical to Cartesian

x = r * sin(theta)
y = r * cos(theta)
z = z

Conversion from Cartesian to Cylindrical

r = sqrt(x^2 + y^2)
theta = tan^-1(x/y)
z = z

A point P can be specified by its Cartesian coordinates (x, y, z) or by its cylindrical coordinates (r, θ, z). The equations above tell you how to convert one set of coordinates to the other.

This problem, however, is about something a bit different. There are unit vectors associated with every point. See, for instance, the illustration on this page. The unit vectors may depend on the coordinates (r, θ, z). The problem is asking you to find the dot product between what's labelled \hat{\theta} on the illustration and the unit vector in the x direction.

A good place to start is figuring out or looking up what the components of a_θ are.

The Attempt at a Solution

I'm just curious if you were my teacher what kind of answer would you want?
I think the point he's trying to prove is that theta is the angle between the x and y plane but I have no idea how to put that mathematically with the given formulas..