Polar Coordinates Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the.

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Presentation transcript:

Polar Coordinates Rectangular (Cartesian) coordinates plot a point by moving left/right and up/down (making a rectangle) Polar coordinates find the same point in a different way r = distance from the origin (radius) θ = angle with positive x-axis

Ex. The Cartesian coordinates of a point are given, find the polar coordinates. (0,1)

Polar  Rect Rect  Polar Ex. The polar coordinates of a point are given, find the Cartesian coordinates. (2,π)

Ex. Find the polar equation for the curve. x2 + y2 = 3y x3y2 + ln y = 3

Ex. Find the Cartesian equation for the curve. r = cos θ sin θ = r2 cos θ

Ex. Sketch the polar equation r = 3

Ex. Sketch the polar equation θ =

Ex. Sketch the polar equation r = sec θ.

Ex. Sketch the polar equation r = 2cos5θ

For the function r = f (θ), Ex. Find the points of horizontal and vertical tangency on the graph r = sin θ, 0 ≤ θ ≤ 2.

Pract. 1. Convert the polar point to Cartesian. 2. Sketch the curve r = 2cos θ. 3. Find the slope of the tangent line to r = 1 + sin θ when θ =