How would the graph of such a function look like?

Question

If I have the function $g:\mathbb R\to \mathbb R\times\mathbb R$ $g(t)=(\cos(t), \sin(t))$.

How would I go about plotting its graph? Is there any software I can use? (no need for accuracy, just want the basic idea)

Answer 1

Hint: what is the distance of $(\cos t,\sin t)$ from $(0,0)$?

To answer the software question, I'd recommend GeoGebra.

Answer 2

How do you graph $y=sin(x)$? You plug in some values ($sin(\pi/2)=1, sin(\pi)=0$ etc..) to get points in Cartesian system and approximately join these points to get the graph(most of it guessing). Just like these you plug in $t=0, t=-\pi/4, t=\pi/4$ etc... For example plugging $t=0$ you get a regular (x, y) point coordinate $x=sin(0)=0, y=cos(0)=1$. So make sure your graph passes through the point $(0, 1)$. Note in case of parametric functions there is also the concept direction of the motion. Find info about that in here and online graph plotter here.