Polar Area Worksheet - Polar Area-Rathish Learning Targets I can classify polar graphs by their shape I can find the area of an inner loop(Limacon of a

Polar Area Worksheet - Polar Area-Rathish Learning Targets...

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Polar Area-Rathish Learning Targets - I can classify polar graphs by their shape - I can find the area of an inner loop (Limacon) of a polar curve Introducing Polar Area The formula for finding the area enclosed by the polar curve r between and is given by the formula: A = 1 2 α β r 2 Types of Polar Graphs: Graph of a Circle Equations: r a sin( ) r a cos( ) r a
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Graph of a Limacon Equations: r a b cos( ) r a b sin( ) If b < a the graph of the Limacon has an inner loop If a < b < 2a the graph of the Limacon is dimpled If 2a less than or equal to b the graph is convex, and not a complete circle Graph of a Rose Curve Equations:
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Unformatted text preview: r 2 9sin3 t r a cos n When n is odd, the curve has n petals When n is even, the curve has 2n petals Graph of Lemniscates Equations: r 2 a 2 sin2 r 2 a 2 cos2 Practice Problems: 1.Determine what type of polar curve is generated from the following equation: r 6 2sin( ) 2.Determine what type of polar curve is generated from the following equations: r 2sin5 t 3.Determine what type of polar curve is generated from the following equations: r 2 9sin3 t Practice Problems Solutions: 1. Convex Limacon 2. Rose Curve with 5 petals 3. Lemniscate...
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  • Fall '16
  • Mrs. Manley
  • Calculus, Expression, Conic section, polar curve, Convex Limacon

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