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On a sphere with radius $R$, find the length of a loxodrome which starts at the equator and makes an angle $\gamma$ with all the meridians.

(No equations for such a loxodrome are given, and should be derived.)

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    Perhaps you should phrase this as a question and not a command?2011-11-29
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    "(No equations for such a loxodrome are given, and should be derived.)" - cool. Unfortunately you've neglected to say what definition of "loxodrome" you're using.2011-11-29
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    @J.M. : I think the definition of "loxodrome" must be a curve that makes an angle $\gamma$ with all the meridians. The way the question is phrased doesn't seem to leave room for another definition.2011-11-29
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    I [know](http://math.stackexchange.com/questions/15801) perfectly well what a loxodrome is, @Michael; I was subtly nudging OP to show his definitions and hopefully derive the necessary differential equation. Oh well.2011-11-29
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    Just a guess: If $\gamma=0$ then clearly the length of the loxodrome is the distance from pole to pole along a meridian, and obviously the length corresponding to $-\gamma$ is the same as the length corresponding to $\gamma$, and it's also obvious that as $\gamma$ approaches a right angle then the length approaches $\infty$. Anyone who's learned trigonometry knows of a function that is equal to $1$ when the angle is $0$, that has the same value at $\gamma$ as at $-\gamma$, and that approaches $\infty$ as $\gamma$ approaches a right angle. Namely the secant function. Therefore.....2011-11-29
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    .......my initial guess would be the distance from pole to pole along a meridian multiplied by the $\sec\gamma$.2011-11-29
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    He wrote "makes an angle gamma with all the meridians." That might be considered "showing his definitions."2011-11-29
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    @Michael: I guess that's fair and I'm just not feeling charitable today...2011-11-29

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