Sketch of curves defined by parameters

[smoothman]

silly question. didnt know where it was meant to go so i just put it here as safest option:)

suppose a curve C is defined by, r(t) = (sint, cost) with $$0 \leq t \leq 2\pi$$

if a sketch of C was required then would you simply just draw the graphs for sint and cost?

 

[rcgldr]

Based on the equation, it's appears that polar coordinates are being used, where r is the length of the vector, and t is the angle of the vector from the x axis. Sin(t) and Cos(t) are the x and y coordinates of the polar vector. This is a single graph, not two.

 

[matness]

If r(t)=(sint, cost) then x component is sint, y component is cost
which means
x^2+y^2=1 as you know it is a circle
but t is not an angle of the vector from x axis( it is valid for (cost,sint))
For our curve if we take t=0 , we obtain the pt (0,1) which is on the y axis
Therefore in our case t is angle from +y -axis

didnt know where it was meant to go so i just put it here as safest option:)

Not sure but this type of questions are generally discussed at homework section

 

[WWGD]

Just thought that a good idea in order to graph the curve C which you have, as Jeff said, written in polar coords. ,if you do not see of-hand how to graph it, would be to switch back (if/where possible) between polars, to Cartesian coordinates, which are the coordinates I think most people are familiar with in terms of doing graphs.

The coordinate change is given by:

x=rcost
y=rsint

and the inverse maps.