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    Re: 360 degree slide rule trig
    From: Paul Hirose
    Date: 2017 Feb 10, 12:30 -0800

    On 2017-02-09 4:18, I wrote:
    > The opposite problem is the determination of course and distance when
    > easting and northing are known. For this conversion from rectangular to
    > polar coordinates:
    > 1. set C index to longitude difference on D
    > 2. set cursor to cos latitude (red numbers) on S
    > 3. set C index to northing on D
    > 4. read course on black T
    > 5. set course on black S to cursor
    > 6. read distance at C index on D
    In steps 4 and 5, don't round off course to the nearest degree. That can
    cause large distance errors near a cardinal direction. For example, from
    latitude 34° the destination is 66 minutes north and 9 minutes east.
    Multiply the latter by cos 34 (red 34 on S) to get 7.47 miles easting.
    Set left C index to 66 minutes on D. Read true course 6.45° on T at the
    cursor. Set 6.45 on S to hairline. Read 66.5 miles at C index.
    A calculator confirms the solution is accurate. But if you round course
    to 6°, distance increases from 66.5 to 71 miles. The closer to a
    cardinal direction, the more an error in course is magnified.
    Fortunately, trig scale accuracy increases in the same proportion.
    (Graduations are every .05° in my example.) Accuracy won't degrade near
    the cardinal directions if you set and read all values with ordinary
    care and don't round them.
    That precaution is not unique to a slide rule solution. The plane
    sailing distance formula
    distance = DLat / cos TC
    becomes progressively less accurate near 90 or 270 if true course is
    rounded to the nearest degree.

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