11-1

This week we started learning chapter 11. A lot of people thought this chapter was sort of easy, but I didn’t. I think this is one of the hardest chapters we have done so far, and doing the pages in the book for a grade really stresses me out because they are a lot harder and will probably bring my grade down. But, I did understand section 11-1 the best out of all of them. For this, you need to be able to convert things into either polar or rectangular.
Convert to rectangular – x = r cos theta and y = r sin theta
Convert to polar- square root x^2 = y^2 and tan theta = y/x
For these problems, you will be given points.
Example 1.
Give polar coordinates for (1, 1)
1. R= square root 1^2 + 1^2
2. R = +/- square root 5
3. Tan theta = 1/1
4. Theta equals tan^-1 (1/1) = 1
5. Since tan is positive, it goes in the first and third quadrants
6. Quadrant 1 = 45 (from the trig chart) quadrant 3 = 225
7. Answer= (square root 2, 45) and ( -square root 2, 225)
Example 2.
Give rectangular coordinates for (1, pi/6)
1. X = 1cos pi/6 and y= 1sin pi/6
2. These are in your trig chart, 1(0) and 1(1)
3. The answer is (0, 1)