does this help?
https://www.wolframalpha.com/input/?i=plot+x+%3D++cos(4t),+y+%3D+sin(6t)
Let G be the graph of the parametric equations
x = cos(4t),
y = sin(6t).
What is the length of the smallest interval P such that the graph of these equations for all t E P produces the entire graph G?
(The "E" represents the symbol for "is in" that looks kind of like a rounded E)
4 answers
So would the interval be (-inf, 1] ??
But that wouldn't be the right answer since it's asking for a length.
cos(4t) has period pi/2
sin(6t) has period pi/3
so, you get the entire curve using the interval
[0,pi]
as indicated by the note next to the graph at the suggested URL.
sin(6t) has period pi/3
so, you get the entire curve using the interval
[0,pi]
as indicated by the note next to the graph at the suggested URL.
1 answer