The explanation in the wikipedia is quite unconvenient, though.

You'd better draw a circle of diameter 1.

Draw a diameter through the center of the circle. and it meets the circle at A and D.

And from A draw a slant line AB that makes angle

th with the diameter AD.

You get an arc(or arch) BD. And the line segment BD of this arch, or arc is the sine of

th.

And the line AB is the co-sine of

th.

So then what is a tangent? If you draw a perpendicular lineDC from D, and this line DC will be tanget to the circle, and extend AB until it meets the tangential line at C. Now the length DC, is the tangent of

th.

http://blogfile.paran.com/BLOG_17207/20 ... 7_trig.gif
Now with this figure in mind, you can easily see that with angles pi/6, pi/4, pi/3, pi/2 you can draw regular triangle, square, hexagon, and just the diameter itself, respectively, on the circle with little difficulty. And you can

figure out the values of sine, cosine, and tangets of the angles after the Pythagorean formula. I hope this helps. But I'm terribly bad at explaining.

I wanted to make this lengthy and detailed. But I was in a hurry 'cause I have to go home soon and help my wife.

edit:

This definition of the trigonometric functions might be unfamiliar. They are usually defined in terms of radius, rather than diameter. But I thought this is a philological forum and the etymologies fitted the better this way. And the definitions in accord to radius can be easily derived by drawing from the center of the circle a line parallel to AB and using the similarities. A trivial step.

edit again:

Why don't you start reading

Elements in Greek?