1. Polar Coordinates & Polar Graphs (10.4)
March 23rd, 2017

2. Polar Coordinates
*In the polar coordinate system, points are of the form rather than P(x, y), which is used in the rectangular coordinate system. r represents the directed distance from the pole (or origin) to point P and is directed angle from the polar axis (aligns with ).
Not all polar coordinates are unique because of the cyclical nature of So,
and
as -r represented the distance opposite

3. r=directed
distance
(the pole)
Directed angle
polar axis

4. Ex. 1: Plot each of the following points on a polar coordinate plane.B) C) D)

5. Coordinate Conversion
Thm : Coordinate Conversion: The polar coordinates of a point are related to the rectangular coordinates (x, y) of the point as follows. 1. 2.

6. Polar Graphs *Polar graphs should be approached one of four ways:
visualize what the polar equation represents
2) convert the polar equation to rectangular form
3) use graphing calculators on polar mode
*4) make a gigantic table of values (this way is a major bummer)

7. Ex. 2: Graph each of the following polar equations using one of the four methods.B) C) D)

8. Slope & Tangent Lines
Th : Slope in Polar Form: If f is a differentiable function of , then the slope of the tangent line to the graph of at the point is
provided that at

9. Ex. 3: Find the horizontal and vertical tangent lines of

10. *Familiarize yourself with special polar graphs on page 735.