Vector best angle to use to solve for x and y

[EulersNumber]

Hello,

I have a vector that is 15 degrees south of east, which if I understand correctly, puts it at 345 degrees on the unit circle. I do have the magnitude, I'll call it M for simplicity. Is it more accurate to use Mcos(15) or Mcos(345) for the x coordinate? Msin(15) or Msin(345) for y?

Many thanks in advance, much appreciated.

 

[Otis]

Is it more accurate to use Mcos(15) or Mcos(345) for the x coordinate?

Hi. The result is the same either way because the sign of x-coordinates in Quadrant I is the same as in Quadrant IV. With common angles while using a calculator, I'll use the reference angle to get a value. If I'm labeling a diagram or writing code, then I prefer to use the actual angle (to help me remember which direction stuff is pointing).

15 degrees south of east, which if I understand correctly, puts it at 345 degrees

Yes, that's correct.

45º could be either 45º north of east or 45º east of north. Either way, its NE.

If we always rotate counterclockwise, then we're adding 45º and have the following.

45º north of east (NE direction) → 0º plus 45º = 45º
45º west of north (NW direction) → 90º plus 45º = 135º
45º south of west (SW direction) → 180º plus 45º = 225º
45º east of south (SE direction) → 270º plus 45º = 315º
[imath]\;[/imath]

 

[blamocur]

Msin(15) or Msin(345) for y?

[imath]\sin 345^\circ = -\sin 15^\circ[/imath].

 

[khansaheb]

Msin(15) or Msin(345) for y?

That would be incorrect - as explained in response above (# 3)