Wondermath
  • Wondermath
The positions, p, of two objects, in metres, after t>= seconds are given by the following functions: p1(x)=xcosx+2 and p2=xsinx+1. When are the objects less than 2m apart during the first 20 secs?
Mathematics
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
well, that depends on x ... did you mean that p1(t) = tcost(t) + 2 and p2(t) = tsin(t) + 1 after t seconds?
Wondermath
  • Wondermath
sorry yeah x is t
anonymous
  • anonymous
If so, you want to find |p1(t)-p2(t)| < 2.00

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Wondermath
  • Wondermath
ohh
Wondermath
  • Wondermath
oh so wud i have to use graphing technology to find that?
anonymous
  • anonymous
Not necessarily you can derive a crazy trig identity like: sin(x)-cos(x) = -sqrt(2) (sin (x - pi/4)
mathmate
  • mathmate
Assuming \[p1(t)=t \cos(t)+2\ and\ p2(t)=t \sin(x)+1\] Then |p1(t)-p2(t)| <2 has 7 intervals between 0 and 20 seconds. You can find them analytically, and preferably graphing first.
anonymous
  • anonymous
are your trig functions cosine and sine expecting Degrees or Radians?
Wondermath
  • Wondermath
radians
Wondermath
  • Wondermath
hmm lemme try this
Wondermath
  • Wondermath
thanks
Wondermath
  • Wondermath
thanks guys i got it!
mathmate
  • mathmate
You're welcome! :)

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