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Try graphing this on the TI-89.

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Presentation on theme: "Try graphing this on the TI-89."— Presentation transcript:

1 Try graphing this on the TI-89.

2 To find the slope of a polar curve:
We use the product rule here.

3 To find the slope of a polar curve:

4 Example:

5 Area Inside a Polar Graph:
The length of an arc (in a circle) is given by r . q when q is given in radians. For a very small q, the curve could be approximated by a straight line and the area could be found using the triangle formula:

6 We can use this to find the area inside a polar graph.

7 Example: Find the area enclosed by:

8

9 Notes: To find the area between curves, subtract: Just like finding the areas between Cartesian curves, establish limits of integration where the curves cross.

10 When finding area, negative values of r cancel out:
Area of one leaf times 4: Area of four leaves:

11 To find the length of a curve:
Remember: For polar graphs: If we find derivatives and plug them into the formula, we (eventually) get: So:

12 There is also a surface area equation similar to the others we are already familiar with:
When rotated about the x-axis: p


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