Engineering Calculus Notes 168

Engineering Calculus Notes 168 - (a r = 3cos θ(b r = sin 3...

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156 CHAPTER 2. CURVES x y z Figure 2.24: Circle of radius 1 about the Origin in the Plane y + z = 0. (d) The lower branch of the hyperbola 4 y 2 x 2 = 1. 2. Sketch the curve traced out by each function −→ p : R R 2 : (a) −→ p ( t ) = ( t, sin t ) (b) −→ p ( t ) = (cos t,t ) (c) −→ p ( t ) = (3 cos t, sin t ) (d) −→ p ( t ) = ( t cos t,t sin t ) (e) −→ p ( t ) = ( t + sin t,t + cos t ) 3. Sketch the curve given by the polar equation:
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Unformatted text preview: (a) r = 3cos θ (b) r = sin 3 θ (c) r = sin 4 θ (d) r = 1 − cos θ (e) r = 2cos 2 θ 4. Parametrize each of the curves in R 3 described below: (a) The intersection of the plane x + y + z = 1 with the cylinder y 2 + z 2 = 1...
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