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

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jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3For 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...

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Notice that \[x = 4\cos t \Rightarrow x^2 = 16\cos^2 t\]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Also, \[y = 4\sin t \Rightarrow y^2 = 16\sin^2 t \]

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Then, (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!

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3Any questions? That was a pretty tricky method. @egbeach

jtvatsim
 one year ago
Best ResponseYou've already chosen the best response.3No problem. Good luck!
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