A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 10 months ago
can anyone explain problem $1I3 from problem set 3? That is: "Describe the motions given by each of the following position vector functions, as t
goes from −∞ to ∞. In each case, give the xyequation of the curve along which P travels,
and tell what part of the curve is actually traced out by P ." The first curve given is r(t) = 2*cos^2 t i + sin^2 t j. I read the solution buit don't quite get the last step
 10 months ago
can anyone explain problem $1I3 from problem set 3? That is: "Describe the motions given by each of the following position vector functions, as t goes from −∞ to ∞. In each case, give the xyequation of the curve along which P travels, and tell what part of the curve is actually traced out by P ." The first curve given is r(t) = 2*cos^2 t i + sin^2 t j. I read the solution buit don't quite get the last step

This Question is Closed

phi
 10 months ago
Best ResponseYou've already chosen the best response.1Problem 1I3 (a) says \[ \vec{r} = < 2\cos^2 t , \ \sin^2 t> \] in other words, r is a position vector with x component = 2 cos^2 t and a y component = sin^2 t The attached graph show the locus of points we create as we increment t notice if we start with \[ x= 2 \cos^2 t \\ y= \sin^2 t \] and (because we want to use sin^2( t) + cos^2(t) = 1 to simplify the equation) we multiply the 2nd equation by 2 and add the two equations: \[ x + 2y = 2\cos^2 t + 2 \sin^2 t \\ x+2y= 2(\cos^2 t + \sin^2 t) \\ x+2y= 2 \] that is the equation of a line. In slopeintercept form \[ y =  \frac{1}{2} x +1 \] so we should expect the locus of points to lie on this line (and it does) because sin and cos are cyclical, we will get cyclical behavior... the point moves back and forth between (0,1) and (2,0)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.