Q. How many times does pi go into a circle?
A. Two times. And that is the same as going 360 degress.
Q. Then half a circle is has one pi?
Q. So pi is like 180 degrees?
A. Right, and Cos of 180 degress is Cos 6pi/6. And that is like having a trinangle that has no opposite edge. Such a triangle is not much of a triangle, O / H is zero.
Q. So what is Cos 6pi/6?
A. It is A/H where A and H are the same lenght, only we are going in a negative direction for A (relative to the X axis).
Q. That means Cos 6pi/6 is -1?
A. That's right.
Q. Okay, that takes care of Cos 6pi/6, what about Cos 7pi/6?
A. Well, that's like going 1/6th of pi (where pi is 180 degrees) farther than we already have. We've gone 6pi/6 to sweep half a circle, now we go a little more beyond that.
Q. So that would be 30 degrees more, right?
A. Right, becasue six times 30 is 180, and we want 1/6th more of that; so we go the extra 30 degrees to make 7/6th of pi.
Q. So we are talking about a triangle with a 30 degree angle?
A. That's right, and it is drawn along the negative x axis below it.
Q. So how do I find Cos 30 degrees?
A. You can draw a 30 degree triangle with a protractor and measure the ratio of A/H.
Q. So will it be positive or negative?
A. Even though it is a 30 dgree triangle, it has been layed along the X axis on the negative side. So A will be negative in the A/H ratio.