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Unformatted text preview: x = 1 3 ± r29 9 = 1 3 ± √ 29 3 i. (2) (a) Please sketch the area enclosed by the polar curve r ( θ ) =  sin θ  . (3 points)21.510.5 0.5 1 1.5 21.510.5 0.5 1 (b) Please compute the area of the ‘ﬂower’ described by the polar curve r ( θ ) = 5sin(7 θ ). (3 points)107.552.5 2.5 5 7.5 1052.5 2.5 5 We use the formula for the area enclosed by a polar curve: 1 2 Z 2 π (5sin(7 θ )) 2 dθ = 1 2 Z 2 π 2510 sin(7 θ ) + sin 2 (7 θ ) dθ = 1 2 ± 25 · 2 π + 10 7 cos(7 θ )  2 π + 1 2 Z 2 π 1cos(14 θ ) dθ ² = 1 2 ± 50 π + 1 2 · 2 π1 28 sin(14 θ )  2 π ² = 51 2 π 2 Good Luck! 3...
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 Fall '08
 Justin
 Math, Complex number, Imaginary unit, Henning Hohnhold

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