lec32 - Lecture 32 18.01 Fall 2006 Lecture 32: Polar...

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Unformatted text preview: Lecture 32 18.01 Fall 2006 Lecture 32: Polar Co-ordinates, Area in Polar Co-ordinates Polar Coordinates r θ Figure 1: Polar Co-ordinates. In polar coordinates, we specify an object’s position in terms of its distance r from the origin and the angle θ that the ray from the origin to the point makes with respect to the x-axis. Example 1. What are the polar coordinates for the point specified by (1 ,- 1) in rectangular coordinates? r (1,-1) Figure 2: Rectangular Co-ordinates to Polar Co-ordinates. r = 1 2 + (- 1) 2 = √ 2 π θ =- 4 In most cases, we use the convention that r ≥ and ≤ θ ≤ 2 π . But another common convention is to say r ≥ and- π ≤ θ ≤ π . All values of θ and even negative values of r can be used. 1 Lecture 32 18.01 Fall 2006 r θ x y Figure 3: Rectangular Co-ordinates to Polar Co-ordinates. Regardless of whether we allow positive or negative values of r or θ , what is always true is: x = r cos θ and y = r sin θ For instance, x = 1 , y =- 1 can be represented by r =- √ 2 , θ = 3 π : 4 1 = x =- √ 2 cos 3 π and- 1 = y =- √ 2 sin 3...
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This note was uploaded on 02/27/2009 for the course MATH 155b taught by Professor Staff during the Fall '08 term at Vanderbilt.

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lec32 - Lecture 32 18.01 Fall 2006 Lecture 32: Polar...

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