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Vector Valued Functions

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?

Solution Preview

We know that the equation (cos theta)^2+(sin theta)^2=1 is an identity. ...