# Homework Help: Polar to Cartesian Unit Vectors in 2D

1. Jan 27, 2013

### leahc

1. The problem statement, all variables and given/known data
Solve for the unit vectors x-hat and y-hat in terms of r-hat and phi-hat.

2. Relevant equations
r-hat=cos(phi)x-hat+sin(phi)y-hat
phi-hat=cos(phi)y-hat-sin(phi)x-hat,

3. The attempt at a solution
I have been working on this for a really long time, and I keep getting a really complicated expression for x-hat, with everything over cos(phi)^2. That seems wrong, and I can't figure out how to solve it from only those two given equations.

2. Jan 28, 2013

### haruspex

Let $\hat{x} = \alpha\hat{r} + \beta\hat{\phi}$.
Compute $\hat{x}.\hat{r}$ etc.

3. Jan 28, 2013

### leahc

I understand that, but how do I compute α and β?

4. Jan 28, 2013

### vela

Staff Emeritus
Haruspex already told you how. That's a dot product in case you didn't recognize it.

5. Jan 28, 2013

### NemoReally

Where did you get those equations? Why did you choose them? Take one example of an x-y unit vector and calculate r and phi - plotting it might help. Then take a different example and do likewise. Notice anything?