# X and y components of polar unit vectors.

1. Jan 31, 2012

### jhosamelly

1. The problem statement, all variables and given/known data
What are the x- and y-components of the polar unit vectors $\hat{r}$ and $\hat{\theta}$ when
a. $\theta$ = 180°
b. $\theta$ = 45°
c. $\theta$ = 215°

2. Relevant equations

3. The attempt at a solution
Please check if I'm correct, i'll just show my answer for a since the process is the same for a, b and c

for a.

$\hat{r_{x}}$ = r cos $\theta$
$\hat{r_{x}}$ = 1 cos 180°
$\hat{r_{x}}$ = -1

$\hat{r_{y}}$ = r sin $\theta$
$\hat{r_{y}}$ = 1 sin 180°
$\hat{r_{y}}$ = 0

in terms of theta... i don't have any idea how... please help

Last edited: Jan 31, 2012
2. Jan 31, 2012

### tjackson3

That's exactly right. If you imagine a unit circle, at 180 degrees, you're on the opposite side of the circle from 0 degrees. x = -1, y = 0.

3. Jan 31, 2012

### jhosamelly

What about theta?? who could I find its x and y component?

4. Jan 31, 2012

### jhosamelly

Can someone help me how to find $\hat{\theta}$? I don't know how. thanks

5. Jan 31, 2012

### SammyS

Staff Emeritus
Do you not have a definition of the unit vector $\hat{\theta}\,?$

The unit vector $\hat{\theta}$ lies in the xy-plane and is 90° counter-clockwise from $\hat{r}\,.$

6. Jan 31, 2012

### jhosamelly

I didn't really get what you said. sorry. can you show me an example on how to get x and y component for a then i'll do it for b and c. thanks. much appreciated.

7. Jan 31, 2012

### SammyS

Staff Emeritus
Well, if $(\hat{r})_x=\cos(\theta)\,,\text{ then }(\hat{\theta})_x=\cos(\theta+90^\circ)\,.$ ... etc.

Use the angle addition identity to simplify cos(θ+90°) .

8. Jan 31, 2012

### jhosamelly

so for a

$(\hat{\theta})_x=cos(180+90)$
$(\hat{\theta})_x=cos(270)$
$(\hat{\theta})_x= 0$

then

$(\hat{\theta})_y=sin (180+90)$
$(\hat{\theta})_y=sin (270)$
$(\hat{\theta})_y= -1$

am i correct?

9. Jan 31, 2012

### SammyS

Staff Emeritus
Yes. That's correct.

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