# Homework Help: Sketching the Image of a Multivariable Function

1. Jul 9, 2012

### Freye

1. The problem statement, all variables and given/known data
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 Im on a foreign keyboard and cant figure out how to get closed brackets).

2. Relevant equations
Unsure

3. 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.

2. Jul 9, 2012

### LCKurtz

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.

3. Jul 9, 2012

### 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.

4. Jul 9, 2012

### LCKurtz

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.