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Published byMollie Banister Modified over 4 years ago

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**Warm Up No Calculator A curve is described by the parametric equations**

x = t2 + 2t, y = t3 + t2. An equation of the line tangent to the curve at the point where t = 1 is 3) A particle moves along the x-axis so that at any time t > 0 the acceleration of the particle is a(t) = e-2t . If at t = 0 the velocity of the particle is 5/2 and its position is 17/4, then its position at any time t > 0 is x(t) =

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**Graphing Polar curves without a calculator**

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Use your calculator to make generalizations… Graph various values of each scalar (a, b and n), then generalize. 1. a) r = a b) r = acos θ c) r = asin θ Generalizations that will help you graph each without a calculator:

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**These are called “cardioids”**

2. a) r = a b cos θ b) r = a b sin θ If a = b, generalizations that will help you graph without a calculator… These are called “cardioids”

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**2. a) r = a bcos θ b) r = a bsin θ**

If a < b, generalizations that will help you graph without a calculator… These are called “limaçons”

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**2. a) r = a bcos θ b) r = a bsin θ**

If a > b, generalizations that will help you graph without a calculator… These are called “limaçons with an inner loop”

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**3. a) r = acos(nθ) b) r = asin(nθ)**

If n is an odd number, generalizations that will help you graph without a calculator… If n is an even number, generalizations that will help you graph without a calculator… These are called “rose curves”

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**Where do the graphs intersect?**

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**Where do the graphs intersect?**

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Paige McNaney, Luke Glaser, Freeman Judd. Vocabulary Polar Curves: 1. Cardioids 2. Limacons 3. Rose Curves Parametric Equations: 1. Parameter 2. Orientation.

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