Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I am given the function $x^2+y^2=25$, and I am suppose to write this as a vector valued function.

I have always been awful at these sort of problems, even with parametric equations, which requires the same process. I just don't understand the concept of "just let x=t;" in this particular case, that just doesn't seem to work.

share|improve this question
add comment

1 Answer 1

up vote 3 down vote accepted

Do parametrization $$ x = 5\cos t \\ y = 5\sin t $$ so your vector valued function is $$ \mathbf r(t) = 5(\cos t\ \hat{\mathbf i}+\sin t \hat{\mathbf j}) $$

share|improve this answer
    
How did you know what to set $x$ and $y$ to? Through practice? –  Mack Feb 25 '13 at 23:56
    
Almost certainly. You can always set one of the variables to $t$, and then solve for the other one -- but you will get a more complicated, multi-part expression. –  user7530 Feb 26 '13 at 0:01
    
@EliMackenzie If I see something like $x^2+y^2$ I immediately switch to polar coordinates, i.e. $\sin$ and $\cos$ since $\sin^2t+\cos^2t = 1$. If it's $x^2-y^2=1$ then I do $\cosh t$ and $\sinh t$ substitution, since, again $\cosh^2t - \sinh^2t = 1$. As for which is which, it doesn't really matter. I could do $x = 5\sin t, y = 5\cos t$ and it'd be the same. –  Kaster Feb 26 '13 at 0:06
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.