Question

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?

Answer 1

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

Answer 2

sorry yeah x is t

Answer 3

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

Answer 4

ohh

Answer 5

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

Answer 6

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

Answer 7

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.

Answer 8

are your trig functions cosine and sine expecting Degrees or Radians?

Answer 9

radians

Answer 10

hmm lemme try this

Answer 11

thanks

Answer 12

thanks guys i got it!

Answer 13

You're welcome! :)