Understanding converting a vector field to cartesian coords

[shemer77]

Homework Statement

Here is the problem and solution but I am confused as to part B
http://gyazo.com/e77d05fc67cb6ac266ff021ef88052dc

The Attempt at a Solution

I understand the first part, but I am totally lost on how they reached their cartesian answer for part B. Firstly why did they do what they did, and secondly where did 36 degrees come from?

I feel like their is some sort of equation or something I am not understanding.

 

[Dick]

Homework Statement

Here is the problem and solution but I am confused as to part B
http://gyazo.com/e77d05fc67cb6ac266ff021ef88052dc

The Attempt at a Solution

I understand the first part, but I am totally lost on how they reached their cartesian answer for part B. Firstly why did they do what they did, and secondly where did 36 degrees come from?

I feel like their is some sort of equation or something I am not understanding.

36 degrees is 0.2π. It's the angle the gave you for phi. Does that help? Other than that they are just using that if u is a unit vector then the component of D along u is (D.u)u.

 

[shemer77]

Hmm ok but why does he have .5 twice as in .5(ap.ax)ax +.5(ap.ax)ay?

 

[Dick]

Hmm ok but why does he have .5 twice as in .5(ap.ax)ax +.5(ap.ax)ay?

One term finds the ax component of 0.5ap and the other finds the ay. Are you sure you understood the first part?

 

[shemer77]

hmm okay thanks I think I figured it out. All I did was use the equations x = p*cosphi, y=p*sinphi and plugged those into the original equation which was already in cartesian for me.