Notation problem

[Imum Coeli]

Let D={(x,y)|4x^2+y^2<=4, x>=0, y>=0}. Consider the transformation T(r,theta) = (r*cos(theta), 2r*sin(theta)).

Now I want to describe a region R in terms of (r, theta) such that T(R) = D and T:R maps to T(R) is 1-1.
I was wondering if this is the correct notation;

R = {(r*cos(theta), 2r*sin(theta)) | 0<=r<=1, 0<=theta<=pi/2}

Thanks.

 

[HallsofIvy]

Let D={(x,y)|4x^2+y^2<=4, x>=0, y>=0}. Consider the transformation T(r,theta) = (r*cos(theta), 2r*sin(theta)).

Now I want to describe a region R in terms of (r, theta) such that T(R) = D and T:R maps to T(R) is 1-1.
I was wondering if this is the correct notation;

R = {(r*cos(theta), 2r*sin(theta)) | 0<=r<=1, 0<=theta<=pi/2}

Thanks.

Yes, that is correct.

 

[JohnZ]

your R = {(r*cos(theta), 2r*sin(theta)) | 0<=r<=1, 0<=theta<=pi/2}
is more like T(R) but not R.
Transformation T from R to D is the function that maps points in R to points in D.
T(r, theta) = (r*cos(theta), 2r*sin(theta)) = (x, y) for any (r, theta) in R