Thread: Tell me about trigonometric functions

Originally Posted by thegnome54

My teachers tried to teach it to me this way, too. The only problem is, it makes no sense - you end up memorizing a meaningless acronym without understanding the concepts. When it comes time to rederive the formulas and such, you might mix up the letters of the acronym!

Granted, some things just have to be memorized - conventions and such, and this is quite close to these most basic principles. Still, though, I personally prefer the "COsine means NEXT TO" logic. It's much harder to fuzz up with time.

Hopefully.

Damn I was expecting thegnome to reply, but I was also expecting there to be some long post with helpful information. (he usually really good at that lol)

Some Old Hippie
Caught Another Hippie
Trippin' On Acid

Now, I don't like those kinda memory things. But my Gr. 10 teacher used that one, and I found it amusing.

Originally Posted by ExoByte

Some Old Hippie
Caught Another Hippie
Trippin' On Acid

Now, I don't like those kinda memory things. But my Gr. 10 teacher used that one, and I found it amusing.

Lol.

Originally Posted by Sandform

Damn I was expecting thegnome to reply, but I was also expecting there to be some long post with helpful information. (he usually really good at that lol)

Haha, alright, I'll try my hand at explaining radians to you.

You probably know how degrees work quite well already - take a 90 degree angle, for example.

A ninety degree angle can be drawn onto a circle so that one quarter of the circle's circumference is penned in, right? This piece of the circumference is called an arc. If you draw a bigger circle, then a ninety degree angle will make a bigger arc - and vice versa. However, no matter how big or small the circle is, a ninety degree angle will always take up the same portion of the circumference - one fourth of it.

Radians measure the size of this arc (which is the length of the circumference that is 'penned in' by a certain angle placed at the center of the circle, remember) instead of measuring the size of the angle itself. But there's a problem - if you take a big circle versus a smaller one, the arc encompassed by a certain angle will always be larger! How do you make sure that you get the same amount of circumference for a certain angle, no matter how big the circle is?

The solution is to change your units - instead of measuring in inches or centimeters, you need to use a unit which changes depending on the size of the circle. And, what is the most obvious choice for such a unit? The radius of the circle.

This makes sense, because the circumference of a circle is 2(pi)radius. This means that there is a linear relationship between radius and circumference. So, you take a big circle (say a radius of 100 units) and a small circle (radius of one unit). You put ninety degree angles in the centers of both. Since the angle takes up a quarter of the circumference of each circle, and the large circle has a circumference of 2(pi)(100), the arc it encompasses on the large circle will be 2(pi)(25). By the same reasoning, the arc on the little circle will be 2(pi)(.25). As you can see, the values are quite different - this is a poor way of telling what angle you're using!

Here we implement our solution - we count by radii! This gives us 2(pi)(25)/100 for the big circle, which simplifies to 2(pi)(.25), and 2(pi)(.25)/1 for the smaller circle, which simplifies to 2(pi)(.25)! IT WORKS! The values are the same, and you can use this as a measure of angles!

A radian, then, is the angle which describes a segment of circumference equal to the radius of the circle. Basically, if you took the radius and put it along the outside of the circle, the angle formed when you make lines from the ends of this segment to the center of the circle is called a radian.

As you know, there are 2(pi)radii in the circumference of any circle. This means that there are 2(pi)radians in a circle, too!

So, how do you convert from radians into degrees? Well, we know that there are 2(pi)radians in a circle, and we know that there are 360 degrees. It would make sense to divide the former by the latter - (2(pi)radians)/360. This can be simplified, though, by getting rid of the "2" on top. This gives us: pi(radians)/180 = degrees.

If you want to solve that equation for radians, you get 1 radian = 180/(pi) degrees. This means that a radian is about 57.3 degrees on any circle.

Hopefully I didn't lose you or oversimplify, I don't really know how far you've been in this area. Enjoy

Originally Posted by thegnome54

This means that a radian is about 57.3 degrees on any circle.

Hopefully I didn't lose you or oversimplify, I don't really know how far you've been in this area. Enjoy

Helpful info there. and nope you didn't lose me hehe, oversimplify...lol no, some of the things you could have jumped over in regard to me, but for those just learning it I think that is like the most perfect explanation i've ever heard...probably because my first teach Mr. grey explained it similarly to you, thus I have a predisposition to like it lol.

Most of the information you guys have given has been review (as it should be for meh heh, i've taken both halves of this already, I just had to do them backwards....I learned the second half first and the first half last)

Switching around schools all the time takes its toll on you after a while. Damn it all! hehe =P I can't wait till i'm 18 and can legally live on my own.

Oh well.