thabomb109
New member
- Joined
- Oct 12, 2016
- Messages
- 1
Alright so I've been given two curves that are given by parametric equations, x=3cos(t) and y=4sin(t) and x^l =4sin(t)and y^l =3cos(t). Both have domain t:[0,2pi]. The questions are
1) Find the number of intersection points and
2)Do they ever cross at the same time?
First step I did was to get a picture of what the equations give. I used geogebra (great service for graphing in 3-d if you need it), and got
< link to objectionable page removed >
. That right there would give you the intersection points but I need to prove where they are, how I got them, and what equations I used. So I plugged in x=x^l and got that t=0.6435 +npi(this step actually answers the second question as well as part of the first). It's bounded by 2pi so the two lines intersect when t=.6435 and 3.7851. Now I'm having trouble proving that the two lines intersect at point A and B in the image. I've tried keeping the two t's as separate variables, t and t^l , but that leads to a seemingly unsolvable equations with inverse cos of sin of cos. I've also tried rewriting the equations in polar form but that also seemed to not do anything. So I'm not quite sure how to get those last two points. Any help is appreciated.
Edit: I should add that when you move the slider for t, the lines equal each other at the same time at the top right and bottom left points but intersect at separate times for A and B.
1) Find the number of intersection points and
2)Do they ever cross at the same time?
First step I did was to get a picture of what the equations give. I used geogebra (great service for graphing in 3-d if you need it), and got
< link to objectionable page removed >
. That right there would give you the intersection points but I need to prove where they are, how I got them, and what equations I used. So I plugged in x=x^l and got that t=0.6435 +npi(this step actually answers the second question as well as part of the first). It's bounded by 2pi so the two lines intersect when t=.6435 and 3.7851. Now I'm having trouble proving that the two lines intersect at point A and B in the image. I've tried keeping the two t's as separate variables, t and t^l , but that leads to a seemingly unsolvable equations with inverse cos of sin of cos. I've also tried rewriting the equations in polar form but that also seemed to not do anything. So I'm not quite sure how to get those last two points. Any help is appreciated.
Edit: I should add that when you move the slider for t, the lines equal each other at the same time at the top right and bottom left points but intersect at separate times for A and B.
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