Class Notes 08.29.2013

Calculus Notes from August 29

1. The first thing that we did was the POD. This problem was concerning Sec 5π / 4. To solve this you could convert to degrees using the conversion 180 / π. This gave you a degree measure of 225. This meant that it was in the third quadrant with a reference angle of 45 degrees. This means that that specific triangle of the bow tie is a 45-45-90 triangle. This also tells you that the two sides across from the 45 degrees are 1 unit and the hypotenuse is root 2. The corresponding trigonometry term for Secant is Cosine. Cosine of the reference angle is -1 / root 2 and so the flip of that (the Secant) would be negative root 2.          (I apologize for "root" but I don't know how to insert that symbol)
2. We then did a questionnaire with an array of personal and math related questions. This was used to see how students can have different interpretations of the same question.
3. Finally, we learned how do go from a distance graph, to a velocity graph, and then to an acceleration graph.
• With a distance versus time graph, you simply plot the points given of distance versus time.
• With the velocity versus time graph, you take the distance traveled per second and plot those points on the graph. So if on the distance graph at 1 second you were at 3 feet and at 2 seconds you were at 7 feet, then the velocity for 2 seconds would be 4 because you traveled 4 feet in that second.
• With the acceleration versus time graph, you draw a tangent line on the velocity graph at each point. Then you take the slope of that line in order to get the acceleration at that particular moment. So if you were to draw a tangent line at 1 second on the velocity graph and that line had a slope of 2, then you would plot an acceleration of 2 and time 1 second.