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    Re: The Bygrave
    From: Hanno Ix
    Date: 2009 Aug 4, 18:29 -0700

    Said a little sloppily:

    The log.cos is always equal to log.sin if you replace the original angle with its compliment to 90 deg. - and vice versa. So, for instance log.cos(40) = log.sin(90 - 40) or = log.sin(50).

    Actually, you can also use log.sin for log.cosec if you put a minus sign before it: log.cosec = -log.sin. Finally, log.sec = -log.cos, and v. v.

    Both, log.sec and log.cosec, occur in Ageton's formulas as in HO211. In this case you need, strictly speaking, only one log scale for sight reduction. As a matter of fact, that is the basis of the method used on STARPATH's Emergency Navigation Card. (Very much worth studying in its own right!)

    In a nut shell: the scale stays the same, only the angles attached to it change depending which one of those four functions, sin, cos ,cosec, and sec, you use. (Note: This scale never ever works for expressions containing tan or cotan!)

    So, if you are willing to make those changes mentally form angle to 90-angle  you can use the  scale as is. To avoid such mental operation (and an error source), often the scale is shown with two entries: sin and cos. or sec and cosec. The one is read backwards as compared to the other. You might want to look up tables of those functions.

    However, there is no question: a scale attached with only the particular entry one is interested in is the most convenient. And on a bobbing boat or in a jumpy airplane in the middle of the night convenience could make a big difference.

    Which is the reason the Bygrave was invented to begin with, no?


    --- On Tue, 8/4/09, douglas.denny@btopenworld.com <douglas.denny@btopenworld.com> wrote:

    From: douglas.denny@btopenworld.com <douglas.denny@btopenworld.com>
    Subject: [NavList 9352] Re: The Bygrave
    To: NavList@fer3.com
    Date: Tuesday, August 4, 2009, 4:43 PM

    This is a nice looking scale.
    Is there a corresponding logCos scale of the same scaling factor to go with it?

    Douglas Denny.
    Chichester. England.

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