Circular Functions (Feb. 15, 2008)

Hello everyone it's Roxanne here and I am your scribe for today or shall i say tonight. I know it's pretty late but I just got home and I decided to do this before I forget.

We first started off with reviewing two questions that we should know how to do already. The questions should be on slide 2 if anyone needs to go back and check. For the second question, where it says cos(pi/2-pi/6), remember that cosine is a function and not a value to distribute. Such as the question 2(x+7), where it will equal 2x+14.

On to slide 3, we looked at the sine graph. It shows that if you look at the black wave the origin is zero aka sine θ=0, and as it moves to sine π/2 = 1 the curve goes up by one. Then it goes back on the x axis as it changes to sine π. As it changes to sine 3π/2 = -1, the curve is now at the bottom at -1 on the x axis. Finally, as it changes to 2π, it curve moves back on the x axis where it equals zero. It then repeats itself over and over again. REMEMBER: 1, 2, 3, 4! Therefore, if you change the input of the sine function such as sine x+1, the line would be higher than the orginial which is the black curve. If you change it to sine x-2, it would be below the black curve.

After we looked at slide 4 which shows us the the curve of cosine. But before we started talking about the graph, one of the students suggested that you could look at the the curve as two half circles. One would be on the top and one would be at the bottom. However, this is not true because in fact the curve of cosine behaves differently compared to the sine curve.
In our graphing calculator we put Y1= sin(x) and Y2=√(1-(x-π/2)². It then showed us the the cosine graph with almost, not quite a half circle on the top curve. Therefore, it proves that the curves are NOT two half circles.

We also used our graphing calculator to graph the cosine curve. Remember when using the graphing calculator go to zoom 4 aka the Friendly window. The friendly window does not create distortion such as zoom 6 where it takes the shape of a square rather than a rectangle. Mr. K also said that there are 95 pixels on the x axis and 63 pixels on the y axis. He explained that if subtract 1 from either of them, you get 47 on the x axis and 31 on the y axis. On calculator, it should show for the Xmin=-4.7 and the Xmax=4.7. It should also show Ymin= -3.1 and Ymax= 3.1. These are also the values that we calculated after you subtract by one and divided by two. The reason why you subtract one is because both the 95th pixel and 63rd pixel is counted as the origin.

Well I suppose that is all! Well at least I hope so because I am quite tired and I want to go to bed! So.. see ya later! OH ! I almost forgot, next scribe will be .......... the one and only FRANCIS! (: alrighty, bye folks!