## Angles

- The math convention is that 0 radians is to the east, and number
increase counterclockwise.
- The science and navigation convention is that 0 degrees is to the north,
and angles increase clockwise.
- In earth science or military terminology, you just use degrees for an
azimuth or direction and the correct convention is assumed.
- Computer trig functions expect the argument to be in radians, and the
inverse functions will return radians
- To convert between radians and degrees
- In Excel, use functions "radians" or "degrees", which are what you
want to convert to.
- In Matlab, use "deg2rad" or "rad2deg" functions

- If you have to convert between the math and science conventions, you
have to:
- Shift the origin by 90 degrees, so you have to take the angle and
add or subtract 90
- Reverse the direction, so you take 360-(angle + 90) or 360-(angle
-90)
- To find out what the formula really should be, you can make a
drawing and work it out. Or you can guess one, see if it's right,
and try the other if not. The power of the spreadsheet (or Matlab)
is that such what-if questions are easy to ask and answer.
- Adjust any angles greater than 360 or less than 0 so they are back
in the 0-360 range. You know that 400 degrees is the same as 40
(or -320), but you don't want to report that. You can use an If-then-else
statement.
- You will have to verify the results. You will dx and dy
values, and you should be able to look at them and know the approximate
angle. For example, if dx = -9 and dy=-1, you have a big westward
component of motion and a small southward component. The resultant
should be a little less than 270, so maybe it will be near 260. In
the answer came out 263 or 251, it would be correct; if it was 280,
that's wrong. If it's 220, that is also wrong, since that is
beyond the halfway point between south and west, and the dy would be
bigger (in absolute value) than the dx, which is not the case. You
should check at least 2 or 3 different quadrants.

*last revised 1/12/2016*