Hello everyone! What a class. I'm speechless and somewhat confused, but i gotta say something. So, at the beginning of the class Mr. Kuropatwa put two questions on the board that would become the basis for the whole class. They were y = sin x and y = cos x. Then we had to chart and graph those equations. We then ended up with a pattern with the charts. 0 to 90 degrees had the same values as 90 to 180 degrees just in reverse order. Then it just repeats itself but in the negatives from 180 to 360 degrees and then the whole shindig repeats. When this is graphed it curves up from the x axis, back down, further down and then back up to the x axis. This is what a sine wave sort of looks like:
Then Mr. Kuropatwa went on to talk about the cosine wave. This is basically the sine wave shifted over. Then we come to the part I don't really know how to explain so help me if I'm wrong. The related angles..... So Mr. Kuropatwa proceeded to show us some "Wicked Mental Math" where he said the sine of thirty degrees is one half, the sign of onehundred fifty degrees is one half, the sign of two hundred ten is negative one half and finally the sign of three hundred thirty is negative one half. After we dismissed that he was a human calculator we went on to fine the reason this was like this. After a lot of guessing and forgetting of C.A.S.T. he decided to grace us with the knowledge on how he came to his conclusions of the set of negative and positive halves. We thought back to grade 9 and SOHCAHTOA. He described a right angle triangle with one for the opposite side and two for the hypotnuse.
Sorry not very good in the paint program. Well that's the general look of it. So sine is opposite over hypotnuse, and that is one over two, so one half. Flip that image over to the other side in your minds eye. The numbers haven't changed, it's still the same triangle so 150 degrees is equal to 30 degrees. Then in your minds eye once more flip it down. Now one value does change, the y coordinate. So it becomes negative, and the same if you flip it to the other side of the y axis. Then we moved onto cosine. If we do all this to cosine we find that all the triangles to the left of the y axis are positive and vice versa. Lastly we found out that tangeant is actually sine of theta over cosine of theta (just a little tidbit out of context here; tangeant means touching in one point). But it all ends up fine in the end because our rule of opposite over adjacent is the equivalent of that sine of theta over cosine of theta just in simpler terms.
Well I hope that makes some sense. The next scribe is Jacky S.