1. ## Find vector function

First off i have a problem that the teacher somewhat worked out on the board.
I am not sure how he got the answer.

Find the vector function that represents the curve of intersection of the two surfaces.

The cylinder.
$\displaystyle x^2 + y^2 = 4$

and the surface $\displaystyle z=xy$

Attempt:

$\displaystyle r=2$

$\displaystyle x= 2cost$
$\displaystyle y=2sint$
$\displaystyle z=(2cost)(2sint)$

Now, from here i think the teacher used the product rule? I am not sure.

Solving for z

$\displaystyle z=2sin2t$

I tried the product rule but couldnt get it. Could someone work out the steps on how he got the answer?

Thank you

2. ## Re: Find vector function

Not the product rule - your teacher used the trigonometric identity $\displaystyle \sin{2t}=2\sin{t}\cos{t}$.

- Hollywood

3. ## Re: Find vector function

Originally Posted by hollywood
Not the product rule - your teacher used the trigonometric identity $\displaystyle \sin{2t}=2\sin{t}\cos{t}$.

- Hollywood
That he did. Thank you!