### Video Transcript

Convert the parametric equations π₯
equals three cos π‘ and π¦ equals three sin π‘ to rectangular form.

Remember, the rectangular form of
an equation is one which contains the variables π₯ and π¦ only. So weβll need to find a way to
eliminate the third variable π‘ from our parametric equations. And at first glance, it doesnβt
seem to be a nice way to do so. But letβs recall some trigonometric
identities. We know that cos squared π plus
sin squared π is equal to one. So letβs begin by simply squaring
our expressions for π₯ and π¦.

With π₯, we get π₯ squared equals
three cos π‘ all squared, which is equal to nine cos squared π‘. And so, we can say that cos squared
π‘ must be equal to π₯ squared over nine. Similarly, we can say that π¦
squared is equal to three sin π‘ all squared. We distribute the parentheses and
we find that π¦ squared is nine times sin squared π‘. And then, we divide through by
nine. And we see that sin squared π‘ is
equal to π¦ squared over nine.

Then, if we replace π with π‘ in
our identity, remember that doesnβt change the identity. We see that we can replace cos
squared π‘ with π₯ squared over nine. We can replace sin squared π‘ with
π¦ squared over nine. And then, this is all equal to
one. We next multiply through by
nine. And we find that the rectangular
form of our equation is equal to π₯ squared plus π¦ squared equals nine.