Sketch the vector function *f*(*t*) = < cos *t*, sin *t* >
for

Answer

- Make a table, using values of
*t* for which we can easily find the sine and cosine:

These outline a quarter of a circle, which is what we find when we connect the dots:

If we replace *t* with *θ*, the coordinates (cos *θ*, sin *θ*) describe a point on the unit circle.

- If wanted to trace out the entire unit circle, we'd have to go all the way from
*θ* = 0 to *θ* = 2π.