logistic_guy
Senior Member
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- Apr 17, 2024
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here is the question
A closed curve r is given by r(t)=(x(t),y(t)) and xcost+ysint=p where p(t) is the distance from the origin to the tangent line at r(t).
Show that:
(i) r(t)=(pcost−dtdpsint,psint+dtdpcost)
(ii) ∣r′(t)∣=∣∣∣∣∣dtdp+dt2d2p∣∣∣∣∣
if i take the derivative of p, i don't get any thing useful
−xsint+ycost=dtdp
A closed curve r is given by r(t)=(x(t),y(t)) and xcost+ysint=p where p(t) is the distance from the origin to the tangent line at r(t).
Show that:
(i) r(t)=(pcost−dtdpsint,psint+dtdpcost)
(ii) ∣r′(t)∣=∣∣∣∣∣dtdp+dt2d2p∣∣∣∣∣
if i take the derivative of p, i don't get any thing useful
−xsint+ycost=dtdp