The problem asks me to sketch the curve represented by the vector-valued function.
The vector-valued function is:
r(theta) = cos theta i + 3 sin theta j
The solution in the solution manual has the following:
x = cos theta
y = 3 sin theta
Up to here I understand what is being done.
The next step in the solution manual is: x^2 + y^2/9 = 1 Ellipse
How was this last equation obtained from x = cos theta and y = 3 sin theta?
We know that the equation (cos theta)^2+(sin theta)^2=1 is an identity. ...