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Warm Up No Calculator 2) A curve is described by the parametric equations x = t 2 + 2t, y = t 3 + t 2. An equation of the line tangent to the curve at.

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Presentation on theme: "Warm Up No Calculator 2) A curve is described by the parametric equations x = t 2 + 2t, y = t 3 + t 2. An equation of the line tangent to the curve at."— Presentation transcript:

1 Warm Up No Calculator 2) A curve is described by the parametric equations x = t 2 + 2t, y = t 3 + t 2. 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) =

2 Graphing Polar curves without a calculator

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

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

5 2. a) r = a bcos θb) r = a bsin θ If a < b, generalizations that will help you graph without a calculator… These are called limaçons

6 2. a) r = a bcos θb) r = a bsin θ If a > b, generalizations that will help you graph without a calculator… These are called limaçons with an inner loop

7 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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12 Where do the graphs intersect?

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