Sketching the Image of a Multivariable Function

[Freye]

Homework Statement

Let f:R^2 to R^2 be defined by f(r,theta) = (rcos(theta), rsin(theta))

Sketch the image under f of the set S = (1,2) X (0,pi) (The open brackets should be closed brackets but I am on a foreign keyboard and can't figure out how to get closed brackets).

Homework Equations

Unsure

The Attempt at a Solution

I am unsure how to sketch something going from R^n to R^m in general, so I have no attempt at a solution. Any hints would be greatly appreciated.

 

[LCKurtz]

Homework Statement

Let f:R^2 to R^2 be defined by f(r,theta) = (rcos(theta), rsin(theta))

Sketch the image under f of the set S = (1,2) X (0,pi) (The open brackets should be closed brackets but I am on a foreign keyboard and can't figure out how to get closed brackets).

Homework Equations

Unsure

The Attempt at a Solution

I am unsure how to sketch something going from R^n to R^m in general, so I have no attempt at a solution. Any hints would be greatly appreciated.

The equation S = (1,2) X (0,pi) defines a region S in R². What you need to do is draw a 2D picture of the region in R² that S is mapped to under the function f. Presumably you know whether S is described with (x,y) coordinates or $(r,\theta)$ coordinates.

 

[Freye]

Oic, so essentially I'm going to be drawing a circle with an inner radius of 1 and an outer radius of 2? If so, this question was much easier than I thought. Thanks a lot for your help.

 

[LCKurtz]

Oic, so essentially I'm going to be drawing a circle with an inner radius of 1 and an outer radius of 2? If so, this question was much easier than I thought. Thanks a lot for your help.

If the coordinates for S are polar coordinates, what you are describing is the shape of S, which is the domain, except the upper variable is $\pi$, not $2\pi$. You wouldn't get the whole circles. If I understand the problem correctly, you need a picture of what it is mapped to.