- #1

ForTheGreater

- 22

- 0

## Homework Statement

It's just an example in the textbook. A vector in cylindrical coordinates.

**A**=

**a**A

_{r}_{r}+

**a**A

_{Φ}_{Φ}+

**a**A

_{z}_{z}

to be expressed in cartesian coordinates.

Start with the A

_{x}component:

A

_{x}=

**A⋅a**=A

_{x}_{r}

**a**+A

_{r}⋅a_{x}_{Φ}

**a**

_{Φ}⋅a_{x}**a**=cosΦ

_{r}⋅a_{x}**a**=-sinΦ

_{Φ}⋅a_{x}A

_{x}=A

_{r}cosΦ - A

_{Φ}sinΦ

Looking at a figure of the unit vectors I get it. At the same time I just don't understand why A

_{r}cosΦ isn't enough to get the magnitude of the A

_{x}component.