Question

let C be the curve r(t)=(tcos(2pit),tsin(2pit)) with t>0., Determine all points where C cuts x axis

Answer 1

Cutting the \(x\)-axis occurs where our \(y\) component is \(0\):$$t\sin2\pi t=0$$Immediately we see that \(t=0\) (point \((0,0)\)) is one such point; can you solve \(\sin2\pi t=0\) for \(t\) to find the others?

Answer 2

am i right by saying that regardless of what value we have for t i will get zero, because it is effecivley the sine graph, as 2pi is a full circle?

Answer 3

@groges but e.g. for \(t=1/4\) we have \(\sin\dfrac{2\pi}4=\sin\dfrac{\pi}2=1\) -- which is not \(0\)

Answer 4

oh yes i see. so i could conclude that C cuts the xaxis for all t where t2sin2πt = 0 ?

Answer 5

huh?

Answer 6

Question asks to determine all points where it cuts x-axis.. So this would be all poins where tsin2πt = 0

Answer 7

yes correct. one point is \(t=0\). there are infinitely many points where \(\sin 2\pi t=0\) though :-p

Answer 8

yes all the constants. eg t=0,1,2,3,4..etc :)

Answer 9

@groges not quite... those are solutions but there are more