www.khanacademy.org/math/multivariable-calculus/thinking-about-multivariable-function/ways-to-represent-multivariable-functions/a/parametric-functions

1 Users

0 Comments

29 Highlights

5 Notes

Tags

Top Highlights

ompletes one loop as � tt goes from 0 00 to 2 � 2π2, pi. Looking at the loopy curve, it seems we shift exactly 1 11 to the right after a single loop.

always think about drawing it.

imagine sketching it by trying to draw a circle counterclockwise while someone pushes your hand to the right at a steady velocity.

start with parametric function for a circle:

the point ( 1 , 0 ) (1,0)left parenthesis, 1, comma, 0, right parenthesis,

(−2,0)left parenthesis, minus, 2, comma, 0, right parenthesis,

xx value by − 3 −3minus, 3.

−3

with respect to time, unrelated to the motions

steady increase

cstart color #bc2612, c, end color #bc2612 times � tt to the � xx-component of the function.

� cstart color #bc2612, c, end color #bc2612 times � tt to the � xx-component of the function.

To figure out what the constant should be, we need to know how far right one has moved after completing one loop

s we shift exactly 1 11 to the right after a single loop.

2πc=12, pi, start color #bc2612, c, end color #bc2612, equals, 1, and hence � = 1 2 � c= 2π 1 start color #bc2612, c, equals, start fraction, 1, divided by, 2, pi, end fraction, end color #bc2612.

we need to place bounds on � tt.

our chosen function � ( � ) f(t)f, left parenthesis, t, right parenthesis completes one loop as � tt increases by 2 � 2π

starting

and tracing a circle

1 1

Glasp is a social web highlighter that people can highlight and organize quotes and thoughts from the web, and access other like-minded people’s learning.