## anonymous 4 years ago how can I determine what x and y is from this: $\hat r t=<t+sin\frac12 \pi t+cos \frac12 \pi t>$

1. anonymous

oh I wrote it wrong

2. anonymous

$\hat r t=<t+sin\frac12 \pi t,cos \frac12 \pi t>$

3. anonymous

much better!

4. anonymous

got it

5. anonymous

still something wrong !!

6. anonymous

yeah still wrong $\hat r t=<t+sin\frac12 \pi t,t+cos \frac12 \pi t>$

7. anonymous

8. TuringTest

$t\vec r=<t+\sin\frac12 \pi t,t+\cos \frac12 \pi t>$makes more sense

9. TuringTest

but wait, brb

10. TuringTest

$t\vec r=\langle t+\sin(\frac\pi2 t),t+\cos(\frac\pi2t)\rangle$is this right is 1/2pit the argument of the trig function

11. TuringTest

?

12. TuringTest

and is t being multiplied by r on the left? this notation is confuzzling me

13. anonymous

14. TuringTest

$\vec r(t)=\langle t+\sin(\frac\pi2 t),t+\cos(\frac\pi2t)\rangle$correct?

15. anonymous

yes

16. TuringTest

$\vec r(t)=\langle x(t),y(t)\rangle$so that implies that$\vec r(t)=\langle t+\sin(\frac\pi2 t),t+\cos(\frac\pi2t)\rangle$leads to$x(t)=t+\sin(\frac\pi2t)$$y(t)=t+\cos(\frac\pi2t)$

17. TuringTest

so it is just a matter of identifying the components

18. anonymous

yep. It makes sense now. I initially wrote it without putting a comma in, and i forgot a "t" somewhere which made it more confusing. But yeah that makes perfect sense.

19. TuringTest

no prob, this is not one of the harder parts of vector calculus fortunately :)

20. anonymous

:P