Section 12.5 - The Polar Coordinate System.

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Presentation transcript:

Section The Polar Coordinate System

This is polar. What about rectangular? r = 2 x y

The keys…… PointEquation Rectangular(x, y)y = Polar

Four Translations Point - Polar to Rectangular Point - Rectangular to Polar Equation - Polar to Rectangular Equation - Rectangular to Polar

Point – Polar to Rectangular

Point – Rectangular to Polar

Equation - Polar to Rectangular

Equation - Rectangular to Polar

Shapes of Polar Curves Graphing Polar Curves on Calculator Finding Points of Intersection (Boundaries of Integration)

The Shapes Lines Circles Cardioid Lemniscate Sprial Rose Curves

Lines in rectangular:

The Shapes - Lines Vertical Line Horizontal Line General Line

Circles in rectangular: Centered at the origin: On one of the axis Passing through the origin The general form gets too complicated in other situations.

The Shapes - Circles

The Shapes – Cardioids (Hearts) Note: Extra loop Only if b > a

The Shapes – Lemniscates (Propellers)

The Shapes - Spirals

The Shapes – Rose Curves n even – 2n petals n odd – n petals

Graphing Polar Curves on Calculator 1. Change mode to Polar 2. Hit y = (you’ll see r = indicating polar mode) 3. Enter the equation 4.Graphing once should give you a sense of how to change the x, y and theta constraints.

5. Now change the constraints in WINDOW

Finding Points of Intersection (Boundaries of Integration)

WRONG ANSWER It’s usually better to graph it first.