MathSofiya
how can I determine what x and y is from this:
\[\hat r t=<t+sin\frac12 \pi t+cos \frac12 \pi t>\]
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MathSofiya
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oh I wrote it wrong
MathSofiya
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\[\hat r t=<t+sin\frac12 \pi t,cos \frac12 \pi t>\]
MathSofiya
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much better!
MathSofiya
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got it
mukushla
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still something wrong !!
MathSofiya
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yeah still wrong
\[\hat r t=<t+sin\frac12 \pi t,t+cos \frac12 \pi t>\]
MathSofiya
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how about now?
TuringTest
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\[t\vec r=<t+\sin\frac12 \pi t,t+\cos \frac12 \pi t>\]makes more sense
TuringTest
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but wait, brb
TuringTest
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\[t\vec r=\langle t+\sin(\frac\pi2 t),t+\cos(\frac\pi2t)\rangle\]is this right
is 1/2pit the argument of the trig function
TuringTest
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?
TuringTest
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and is t being multiplied by r on the left?
this notation is confuzzling me
MathSofiya
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no it r(t), my bad
TuringTest
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\[\vec r(t)=\langle t+\sin(\frac\pi2 t),t+\cos(\frac\pi2t)\rangle\]correct?
MathSofiya
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yes
TuringTest
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\[\vec r(t)=\langle x(t),y(t)\rangle\]so that implies that\[\vec r(t)=\langle t+\sin(\frac\pi2 t),t+\cos(\frac\pi2t)\rangle\]leads to\[x(t)=t+\sin(\frac\pi2t)\]\[y(t)=t+\cos(\frac\pi2t)\]
TuringTest
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so it is just a matter of identifying the components
MathSofiya
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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.
TuringTest
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no prob, this is not one of the harder parts of vector calculus fortunately :)
MathSofiya
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:P