## egbeach one year ago Eliminate the parameter. x = 4 cos t, y = 4 sin t

1. jtvatsim

For most of these questions the strategy is to solve one equation for t and plug this into the remaining equation, however, that will be very messy for this one. Instead, you will need to be a little clever and use the fact that $\cos^2 t +\sin^2 t = 1.$ Here's how...

2. jtvatsim

Notice that $x = 4\cos t \Rightarrow x^2 = 16\cos^2 t$

3. jtvatsim

Also, $y = 4\sin t \Rightarrow y^2 = 16\sin^2 t$

4. jtvatsim

Then, (again being very clever) notice that we can add these new equations together to get $x^2 + y^2 = 16\cos^2 t + 16 \sin^2 t$ but this is just $x^2 + y^2 = 16(\cos^2 t + \sin^2 t) = 16(1) = 16$ There the parameter is gone!

5. jtvatsim

$x^2 + y^2 = 16$

6. jtvatsim

Any questions? That was a pretty tricky method. @egbeach

7. egbeach

Thank you!

8. jtvatsim

No problem. Good luck!