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[Vector]

Hah!  The reason why I find this so funny is because I started as a mechanical engineering major.  Then I got tired of the bullshit and ran screaming towards pure mathematics >_>  Give some courses a whirl!

[Virex]

@Vector- two perpendicular lines intersect at 90 degrees. Every angle formed by these two lines is 90 degrees. The slopes of the lines, when multiplied, equal -1, as one is the negative inverse of the other.

@Virex- Thank you for that. I didn't factor in the definition of a circle, as I didn't know exactly what it was. (asides from all points that are a given distance from another point in a 2d plane.) The given definition is also helpful, but I'm not understanding the part below. What does 'It' refer to? The line? If so, do you mean 'it intercepts the tan-line and the x=0 line

It's the intercept of the tan-line and the x=0 line

You're pretty close to what I meant. sec(x) is the lenght of the line segment between the centre of the unit circle and the point where the tangent line, as given in the picture, intercepts the line where Y = 0 (Wups, I realised I said X = 0, which would be the cosecant)

[Heron TSG]

If you want to learn stuff, you can't just come up with completely random ideas and throw them at people and expect them to do the work for you.

I see that now.

Also, now that I've found why tangent lines are placed in the way that they are, that makes sense. As the tangent line approaches the vertical, sec(X) gets incredibly large, which makes sense due to the high Y-intercept of the near-vertical line.

[G-Flex]

You're mixing up sec(x) and csc(x) there.

[Heron TSG]

Yeah, I looked a bit more closely and the 'Sec(X) is the length of the line from the center to the Y-intercept of tangent' definition is kind of odd. A secant (line) is a line connecting two points on a circle. Thus, it can't very well be from the center to the tangent.

[G-Flex]

Errrgh. Now you're getting even MORE confused.

sec(x) IS NOT a line segment connecting two points on a circle. It just isn't. At all. Stop confusing those two.

sec(x) IS, however, two things:

• 1/cos(x)
• What Virex said: The distance between the center of the unit circle and the point where the tangent line (as defined by the angle) intercepts the x-axis. Seriously, just look at the image posted earlier, it's the big thing labeled "sec".

[Heron TSG]

Errrgh. Now you're getting even MORE confused.

Why yes, I am. I'm glad I know what sec(X) is now, but the whole point was to find a correlation between a secant line and the secant function.

[G-Flex]

Since, since it has a relationship to the tangent line, and the tangent line is just a secant line whose chord length approaches 0, I guess you found one.

[Heron TSG]

No, actually, I believe youfound one, and I thank you for it.

I'm going to delve into conic sections for a while, and see if I can't see something wacky with them. Thank you all for your help, and I will probably bring my findings here.

[G-Flex]

Vector found it before I noticed. I just helped explain it.

[Vector]

No, actually, I believe youfound one, and I thank you for it.

I'm going to delve into conic sections for a while, and see if I can't see something wacky with them. Thank you all for your help, and I will probably bring my findings here.

Oh, lovely!  Conic sections are amazing.

Vector found it before I noticed. I just helped explain it.

Thanks    I don't know how I always manage to find interesting crap I can't explain, though.  Makes my life difficult.

[Heron TSG]

Oh, well, thanks to all of you then.  From my experiments with a piece of paper and two party hats, I've found that a hyperbola is formed when a plane intersects the two cones that are tip-to-tip. Hopefully I'll find other cool shapes.

[G-Flex]

  I've found that a hyperbola is formed when a plane intersects the two cones that are tip-to-tip.

That's how every conic section is formed. Planar slices through that sort of double-cone structure.

http://en.wikipedia.org/wiki/Conic_section

[Vector]

  I've found that a hyperbola is formed when a plane intersects the two cones that are tip-to-tip.

That's how every conic section is formed. Planar slices through that sort of double-cone structure.

http://en.wikipedia.org/wiki/Conic_section

Don't spoil it for him!  Let him explore.  He's only 14 or something.

[Heron TSG]

A piece of paper stuck through a party hat at an oblique angle forms a line shaped like a parabola. It would seem that a great many formulas can be replicated in this way.