alright...so I have this Calc lab due...and i've been working at it for the past week...I could answer these all very briefly, but he wants a more in depth analysis, which when we've never gone over these things kind of sucks...I know a large population of MR visitors have taken Calc so i'm looking for any help I can get...
1) What is the difference between a function and a parametric curve? (Many answers are possible - try to give atleast two.)
2) Different parametric equations can represent the same curve. Give an example that demonstrates this fact. Be careful about the domain and direction.
3) Try to guess waht the graph of the following set of parametric equations looks like, and then see if you are right:
x(t)=sin(2t), y(t)=cos(6t), 0<t<4pi
These curves are called Lissajous figures and are used in electrical engineering to see if two signals are "in sync". Explain this.
4) Consider these two sets of parametric equations:
x(t)=t, y(t)= sin(t), 0<t<infinity
and
x(t)=2t, y(t)=sin(2t), 0<t<infinity
Explain the relationship between their associate curves.
1) What is the difference between a function and a parametric curve? (Many answers are possible - try to give atleast two.)
2) Different parametric equations can represent the same curve. Give an example that demonstrates this fact. Be careful about the domain and direction.
3) Try to guess waht the graph of the following set of parametric equations looks like, and then see if you are right:
x(t)=sin(2t), y(t)=cos(6t), 0<t<4pi
These curves are called Lissajous figures and are used in electrical engineering to see if two signals are "in sync". Explain this.
4) Consider these two sets of parametric equations:
x(t)=t, y(t)= sin(t), 0<t<infinity
and
x(t)=2t, y(t)=sin(2t), 0<t<infinity
Explain the relationship between their associate curves.
