L33 Sketching and Area of Polar Curves I

L33 Sketching and Area of Polar Curves I - and outside the...

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Lectire 33: Sketching and Area of Polar Curves Areas in Polar Coordinates Formula for the area of a sector of a circle A = 1 2 r 2 where r is the radius and is the radian measure of the central angle. Area of the polar region bounded by a polar curve r = f ( ) and by the rays = and = is A = R 1 2 r 2 d 1
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ex. Graph the polar curve and nd the area enclosed by the curve: ( 2 ) r = cos 2 2
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ex. Graph the curve and nd the area enclosed: r = 2(1 sin ) (6 ) 3
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ex. Graph the curve and nd the area of the inner loop: r = 1 3 cos : ( 11 2 arccos 1 3 3 p 2) 4
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ex. Graph the curves and nd the area inside the rst curve
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Unformatted text preview: and outside the second curve r 2 . r 1 = 1 + sin ± , r 2 = 1 + cos ± (2 p 2) 5 ex. Sketch the curves and set up the integral(s) for the area of the region that lies inside both curves r 1 = 3 + 2 sin ± and r 2 = 2. ( 19 ± 3 ± 11 p 3 2 ) 6 NYTI: Sketch the curve r = 4 cos 3 ± and ±nd the area it encloses. (4 ± ) 7 ex. Sketch the curve and ±nd the area of the inner loop of r = 1 ± 2 sin ± ( ± 2 ± 3 p 3 2 ) Tonight’s homework: sketch and ±nd area en-closed by polar curves. 8...
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