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Wondermath

  • 5 years ago

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?

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  1. anonymous
    • 5 years ago
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    well, that depends on x ... did you mean that p1(t) = tcost(t) + 2 and p2(t) = tsin(t) + 1 after t seconds?

  2. Wondermath
    • 5 years ago
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    sorry yeah x is t

  3. anonymous
    • 5 years ago
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    If so, you want to find |p1(t)-p2(t)| < 2.00

  4. Wondermath
    • 5 years ago
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    ohh

  5. Wondermath
    • 5 years ago
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    oh so wud i have to use graphing technology to find that?

  6. anonymous
    • 5 years ago
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    Not necessarily you can derive a crazy trig identity like: sin(x)-cos(x) = -sqrt(2) (sin (x - pi/4)

  7. mathmate
    • 5 years ago
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    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.

  8. anonymous
    • 5 years ago
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    are your trig functions cosine and sine expecting Degrees or Radians?

  9. Wondermath
    • 5 years ago
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    radians

  10. Wondermath
    • 5 years ago
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    hmm lemme try this

  11. Wondermath
    • 5 years ago
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    thanks

  12. Wondermath
    • 5 years ago
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    thanks guys i got it!

  13. mathmate
    • 5 years ago
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    You're welcome! :)

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