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[Vector]

First, 8.56x10^8 should be 8.56x10^-8. whoops.

Second, the point (derp.) is that you won't have a secant when it becomes a point. you'll have a point. Therefore, the relationship would still work because it'd be true for all secants.

Third, An inverse relationship is still a relationship. It may not be a function, however. That;d explain the wackiness dividing by zero would entail.

Pseudo-edit: I know I'm probably wrong, I'm just chucking ideas out in hopes of a bullseye. It'd be nice to learn something without extensive help from textbooks and teachers.

... You can't just chuck out ideas in hopes of a bullseye.  To paraphrase my favorite professor ever, you cannot just be curious.  You must be curious and thoughtful.  You have the curious part.  Now you must learn to think, and think well.  Learn to answer your own questions.  That is the true path to becoming a skilled mathematician, for anyone from whom you learn any mathematics whatsoever is still a teacher of some sort.

The definition of a function is that you put an object in and an object comes out.  Dividing by zero has nothing to do with whether or not a relation is a function or not.  The problem with your ideas is one of magnitude, not of the definition of a function.

By the way, a line of zero length is a point.  Thus every point on a circle is a secant line.  Hurr hurr.

[G-Flex]

[quote author=Barbarossa the Seal God
Second, the point (derp.) is that you won't have a secant when it becomes a point. you'll have a point. Therefore, the relationship would still work because it'd be true for all secants.

Third, An inverse relationship is still a relationship. It may not be a function, however. That;d explain the wackiness dividing by zero would entail.

Pseudo-edit: I know I'm probably wrong, I'm just chucking ideas out in hopes of a bullseye. It'd be nice to learn something without extensive help from textbooks and teachers.
[/quote]

I honestly don't know how any of that changes what I said in any way.

[Heron TSG]

Good morning world, it's nice to be not tired now. I'll be spending a while later looking at the equations of various secants on a unit circle (centered at the origin) and the secant of the angle formed by their perpendicular bisectors. (as the perpendicular bisector must go through the center.)

[Vector]

Good morning world, it's nice to be not tired now. I'll be spending a while later looking at the equations of various secants on a unit circle (centered at the origin) and the secant of the angle formed by their perpendicular bisectors. (as the perpendicular bisector must go through the center.)

Wait.  Can you explain why, precisely, this is a good idea?

[Heron TSG]

I want to see if there's a relationship between the slope of the secant's bisector and the value of 1/Cos(X), when X is the angle formed by the bisector.

Theoretically, I could use the equation of the secant itself, but it would involve shifting it to the point that it crosses the origin anyway, if I want to keep it simple.

[Vector]

I want to see if there's a relationship between the slope of the secant's bisector and the value of 1/Cos(X), when X is the angle formed by the bisector.

Theoretically, I could use the equation of the secant itself, but it would involve shifting it to the point that it crosses the origin anyway, if I want to keep it simple.

Wait, I'm sorry.  It's been a long time since I took geometry.  Can you remind me of what "perpendicular" means?

[Pillow_Killer]

Okay

[Vector]

Two lines are concidered perpendicular  if they congruent adjacent angles...

...

No, I'm looking for Barbarossa's answer on this one.  I want him to really think about it.

[Virex]

Unhelpful Picture:

If sec(x) is the length of the secant corresponding to an angle X in said picture, then we get:

sec(x) = (r^2 + tan^2(X)))^0.5  (pythagoras theorem)
sec^2(x) = 1+tan^2(X)  (r=1, because we have a unit circle)

tan(x) = sin(x)/cos(x)  (Alternative definition)
sin^2(x) + cos^2(x) = 1  (definition of a circle)
sin^2(x) = 1-cos^2(x)  (rearanging stuff)

sec^2(x) = 1 + (1-cos^2(x))/(cos^2(x))  (just replacing tan^2(x) with the above defintion)
sec^2(x) = 1/cos^2(x)  (you can divide the other cos^2(x) out)
sec(x) = 1/cos(x), Q.E.D

While I'm leaping over a lot here (my proof isn't going to work the other way around) this does indicate that sec(theta) is just the length of the secant line in the unit circle, for a given value of angle theta. It's the intercept of the tan-line and the x=0 line

[Heron TSG]

@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

[Vector]

No, what I'm saying is... bleh.

What the hell are you doing?  What is the goal here, in essence?

[Heron TSG]

The current goal is to learn why two seemingly unrelated things have the same name, and if they are related. So far, I've learned that they are related. How they are related is the next question.

The overarching goal is to learn more about the world we live in, as opposed to taking everything for granted because our teachers tell us so.

[G-Flex]

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.

If you're wondering something, test it. Then draw conclusions. Then test those conclusions.

[Vector]

*sigh*

Sorry, I'm having trouble following the vein of your reasoning.  This is likely because I've been on 5 hours of sleep a night for the past week and a half.  Also possibly because you formulate things in a funkalicious fashion.

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.

If you're wondering something, test it. Then draw conclusions. Then test those conclusions.

Hmm, you seem like a fellow math major.  Hello, there.

[G-Flex]

I'm a beginning engineering major, which means I only have to prove things within tolerance, so there.

But yeah, I do probably tend to think like a math guy. I get pissed off if something just seems correct if there's some chance it might not be.

That's why, in this drafting course I had to take, I got so annoyed with AutoCAD but liked SolidWorks so much. In AutoCAD, I had to draw lines and shapes of various description and trust later on that I did it right, and could only verify this by having it take measurements to certain precisions. In SolidWorks, I could actually define relationships between parts such that the actual shape would be fully defined by them, guaranteeing them completely no matter how else I screw things up.

Basically, in AutoCAD, I knew two lines were perpendicular and connected at the endpoints because I zoomed in a lot and made sure they sort of looked coincident at the endpoints, and measured the angle and saw "90.000 degrees". In SolidWorks, I knew two lines were perpendicular and connected at the endpoints because I told it that it is the truth here and forever amen and to make sure I never do anything that could change this.