Polar Coordinates & Polar Graphs (10.4)

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Presentation transcript:

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

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

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

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

Coordinate Conversion Thm. 10.10: Coordinate Conversion: The polar coordinates of a point are related to the rectangular coordinates (x, y) of the point as follows. 1. 2.

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)

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

Slope & Tangent Lines Th. 10.11: 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 .

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

*Familiarize yourself with special polar graphs on page 735.