Clicker Question 1 What are two polar coordinates for the point whose rectangular coordinates are (3, 1)? A. (3 + 1, 0) and (-3 – 1, ) B. (3 + 1, /6) and (3 + 1, /3) C. (2, /6) and (2, - /6) D. (2, /3) and (-2, 4/3) E. (2, /6) and (-2, 7/6)

Clicker Question 2 What are the rectangular coordinates of the point whose polar coordinates are (6, -/4) ? A. (6, -6) B. (32, - 32) C. (0, -6) D. (-32, 32) E. (32, 32)

Clicker Question 3 The curve r = 4 sin() with 0     is: A. A straight line through the origin. B. A half circle of radius 2. C. A circle with diameter on the y-axis of radius 2. D. A circle with diameter on the x-axis of radius 2. E. A spiral.

Areas and Arc Lengths in Polar Coordinates (11/7/12) What is the area of a region being swept out as  goes from a to b? Assume as usual that r is a function of . Well, break the region up into small sectors and then add them up!! The answer comes out Why??

Example of Area Find the area of one leaf of the 4-leaf clover r = sin(2). Look at the picture and make a guess first.

Arc Length This is simply a matter (following our work on parametric equations) of translating into polar coordinates. Let’s try it.

Arc Length Continued The answer is Example: What’s the arc length of that single leaf in the previous example?

Assignment for Friday Read Section 10.4 and do Exercises 1, 3, 5, 9, 17, 45, and 47. No new material on Friday. I’ll be available for questions 2-4 on Thursday and 1:40-3:30 on Friday. Test #2 is Monday, Nov 12. It will focus on Chapters 9 and 10. You may (and should!) arrive at 8:30. One reference sheet allowed. Next Wednesday’s class will start at 9:05.