# A7 - R Your sketches in Question.2 may be helpful(a R is...

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Math 128: Assignment 7 due Wednesday, Nov 9 by 4:30 pm Koray Karabina ([email protected]) 1. In parts (a)–(d), plot the point whose polar coordinates are given. Then ﬁnd the Cartesian coordinates of the point. (a) ( - 2 , 5 π/ 4) (b) (1 , 5 π/ 2) (c) (2 , - 7 π/ 6) (d) ( - 1 , - π/ 4) 2. Sketch the polar graphs in parts (a)–(c). Explain and show your work. (a) r = sin(3 θ ) (b) r = 1 - cos θ (c) r = 1 + 2 cos θ 3. Find the points on the polar curve r = 1 + cos θ , where the tangent line is vertical or horizontal. 4. In parts (a)–(c), ﬁnd the areas of the given polar regions
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Unformatted text preview: R . Your sketches in Question.2 may be helpful. (a) R is one leaf of the curve r = sin(3 θ ). (b) R is bounded by the curve r = 1-cos θ . (c) R is the region inside the larger loop and outside the smaller loop of the curve r = 1 + 2 cos θ . 5. In parts (a)–(b), ﬁnd the lengths of the polar curves. (a) r = e aθ ,-π ≤ θ ≤ π (b) r = a (1 + cos θ ) , ≤ θ ≤ 2 π...
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