(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Write the vectors B,D, and F in the figure in Cartesian form, with unit vectors.

(See attachments)

2. Relevant equations

a_{x}= a cos theta

a_{y}= a sin theta

where a = magnitude of vector a, and theta = the angle vector a makes with the positive direction of the x axis

3. The attempt at a solution

I'm having trouble with this "the angle vector a makes with the positive direction of the x axis" business. What does that mean, exactly? The smallest angle that the vector can make with the positive direction of the x axis? Because there are two angles it could make, technically. My book is not specific and I'm confused.

In one part of my book it has a note: "Angles that are measured relative to the positive direction of the x axis are positive if they are measured in the counter clockwise direction and negative if measured clockwise. For example, 210 degrees and -150 degrees are the same angle"

I thought maybe it's just talking about a protractor but then I wondered if it had anything to do with the angle theta business.

So how exactly does one find the angle a vector makes with the positive direction of the x axis?

The thetas I found for the vectors in the images are:

Vector B: 53 degrees

Vector D: 143 degrees

Vector F: I haven't any idea

For Vector B, I arbitrarily decided to use the smaller angle.

For Vector D, I stuck with the smaller angle idea and found theta to be 143 degrees.

For Vector F, I'm puzzled by the addition of the z axis, as our book doesn't have a formula for resolving the vector of a three dimensional vector, or at least we haven't covered it and I haven't found it. I also wonder how I'm supposed to interpret the "the angle the vector makes with the positive direction of the x axis" business on a three dimensional coordinate system.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Converting Polar coordinates to Cartesian coordinates

**Physics Forums | Science Articles, Homework Help, Discussion**