Question

Find the equation in the xy-plane whose graph includes x = 8 sin t and y = 8 cos t.

Answer 1

I got \[y=\sqrt{1-x^2}\]

Answer 2

You are close!

If you calculate x² + y², you get: 64sin²t + 64cos²t=64(sin²t + cos²t)=64*1=64.

So: \( x^2 + y^2 = 64\) and therefore:

\(y^2 = 64 - x^2\), which means: \(y=\pm\sqrt{64-x^2}\).

Answer 3

If you make a drawing, \(y=\sqrt{64-x^2}\) is the upper half of a circle with radius 8 and \(y=-\sqrt{64-x^2}\) is the lower half.

Answer 4

oh, I see. I think I tried to get one equation equal to another to plug in, but then my 8s cancelled and I was left with 1.

Answer 5

Yeah, the 8 blows it up eightfold...

Answer 6

Thanks!

Answer 7

YW!