Trace Curve: x(t)=1+t, y(t)=t/2 0-2

  • Thread starter Thread starter mattmannmf
  • Start date Start date
  • Tags Tags
    Curve Sketch
Click For Summary
SUMMARY

The discussion focuses on tracing the parametric equations x(t) = 1 + t and y(t) = t/2 for t values ranging from 0 to 2. Participants clarify that tracing this curve involves plotting specific points derived from chosen t values, such as t = 0, 0.5, and 1, and connecting these points to visualize the curve. The approach is confirmed to be similar to tracing a curve from 0 to 2π, but without the inclusion of π. Key points include the identification of coordinates at various t values, which are essential for accurate plotting.

PREREQUISITES
  • Understanding of parametric equations
  • Basic graphing skills
  • Familiarity with plotting points on a Cartesian plane
  • Knowledge of the concept of tracing curves
NEXT STEPS
  • Learn how to plot parametric equations in a graphing tool like Desmos
  • Explore the concept of derivatives in parametric equations
  • Study the relationship between parametric equations and Cartesian coordinates
  • Investigate the effects of varying t values on curve shape
USEFUL FOR

Students studying calculus, mathematics enthusiasts, and educators teaching parametric equations and curve tracing techniques.

mattmannmf
Messages
170
Reaction score
0
let x(t)= 1+t and y(t)= t/2

trace (x(t),y(t)) as t advances from 0 to 2.

Im just unsure of how to trace it. Is it pretty much the same thing as tracing it from 0 to 2pi except I am leaving out the pi?

So axis in term of t:
positive x= 0 or 2
positive y= 1/2
negative x= 1
negative y= 1.5
 
Physics news on Phys.org
mattmannmf said:
let x(t)= 1+t and y(t)= t/2

trace (x(t),y(t)) as t advances from 0 to 2.

Im just unsure of how to trace it. Is it pretty much the same thing as tracing it from 0 to 2pi except I am leaving out the pi?

So axis in term of t:
positive x= 0 or 2
positive y= 1/2
negative x= 1
negative y= 1.5

Pick a few values of t (like t=0,1/2,1,etc.) and write down the pairs (x(t),y(t)) for each of them. Plot these points and sketch the curve through them.
 

Similar threads

Replies
2
Views
2K
Replies
6
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
1K
Replies
8
Views
2K
  • · Replies 1 ·
Replies
1
Views
9K
  • · Replies 105 ·
4
Replies
105
Views
11K
  • · Replies 1 ·
Replies
1
Views
2K
Replies
4
Views
2K
Replies
8
Views
2K