View Full Version : The Units of Direction Cosines

07-03-2007, 02:21 AM
Hello All,

I am in the process of revising a manuscript, where a reviewer asked
that I provide units for the direction cosines vectors that I report. I
am not sure how to respond.

The original data describe the orientation of an axis (inclination and
deviation) and are therefore angles described in degrees. Angles are
technically ratios (X over Y), which would make them unit-less values in
their purest form. We give them units when we convert the ratio into
degrees, radians, grads, or whatever. So, I suppose the direction cosine
elements should be expressed in whatever unit was associated with the
ratio that created the angle. But, there are two problems with that.
First, the original data were only measured angles. There were no
explicit X and Y values in whatever units. Second, the direction cosine
is a unit vector and so I am not sure that its elements would need
specific units. As long as the three elements of the vector combine to
form a vector of length 1, I don't think it really matters if that unit
is in Angstroms, Light-Years, or anything in between.

So, first question: what are the appropriate units for the elements of a
direction cosines vector?

And, assuming that you have as much difficulty as I in answering that
first question, how would you respond to this reviewer's request?

Thomas M. Greiner, Ph.D.

Assistant Professor of Anatomy

Dept. of Health Professions

University of Wisconsin - La Crosse

1725 State Street

La Crosse, WI 54601 USA

Phone: (608) 785-8476

Fax: (608) 785-8460