pset7 - Problem Set 7 Math 486-W10 Yvonne Lai Relevant concepts Arithmetic of parametric equations If you dont have a calculator that plots parametric

pset7 - Problem Set 7 Math 486-W10 Yvonne Lai Relevant...

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Problem Set 7 Math 486-W10 Yvonne Lai Relevant concepts: Arithmetic of parametric equations If you don’t have a calculator that plots parametric equations in polar coordinates, try http: //fooplot.com . Notes on using this site are attached to the end of this problem set. Polar Coordinates, parametric equations in polar coordinates. See end of problem set. Presenters have received emailed instructions. Non-presenters are responsible for all problems, due Friday Feb 26, 2010, 5:30pm at my office door (1856 EH). 1.Adding parametric equations. Suppose that you have two parametrized paths, and at timet, the firstpath has positionz1and the second parametrization has positionz2. Then the addition of these twoparametrizations should give a path that has positionz1+z2at timet.Let(r1(t),θ1(t))and(r2(t),θ2(t))be the two parametrizations. Then in Cartesian form,(r1(t),θ1(t)) =r1(t)(cosθ1(t) +isinθ1(t))and(r2(t),θ2(t)) =r2(t)(cosθ2(t) +isinθ2(t)).So the addition of these two parametrizations is the path(r(t),θ(t))where(r(t),θ(t))|{z}path in polar form= (r1(t)cosθ1(t) +r2(t)cosθ2(t)) +i(r1(t)sinθ1(t) +r2(t)sinθ2(t))|{z}path in Cartesian form.(a) Draw(10, 2t) +20ifor 0t2π. Describe the path in a sentence (where it starts, ends, howmany times it winds around, geometric shape, center).

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