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A region R in the xy-plane is given. Find equations for a transformation T that maps a rectangular region S in the uv-plane onto R, where the sides of S are parallel to the u- and v- axes. (Let u play the role of r and v the role of θ. Enter your answers as a comma-separated list of equations.) R lies between the circles x^2 + y^2 = 1 and x^2 + y^2 = 3 in the first quadrant

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Answer:

[tex]x = u\cos(v) , y = u \sin(v)[/tex]

Step-by-step explanation:

For that transformation you just have to use polar coordinates, notice that when you use polar coordinates the radius is constant when the angles varies and the angle is constant when the radius varies. Therefore your transformation would be just

[tex]x = u\cos(v) , y = u \sin(v)[/tex].