## 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?

1. anonymous

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

sorry yeah x is t

3. anonymous

If so, you want to find |p1(t)-p2(t)| < 2.00

4. Wondermath

ohh

5. Wondermath

oh so wud i have to use graphing technology to find that?

6. anonymous

Not necessarily you can derive a crazy trig identity like: sin(x)-cos(x) = -sqrt(2) (sin (x - pi/4)

7. 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.

8. anonymous

9. Wondermath

10. Wondermath

hmm lemme try this

11. Wondermath

thanks

12. Wondermath

thanks guys i got it!

13. mathmate

You're welcome! :)