# Thread: Application of Trig. Graphs

1. ## Application of Trig. Graphs

Two particles (A and B) move on a straight line and their position (x metres) from the origin O at time t hours is givne by x = sint and sin2t respectively. Write down an interval of time in which both particles are travelling towards the origin with positive velocity.

Could someone please explain to me how on earth to do this question?

2. Hello xwrathbringerx
Originally Posted by xwrathbringerx
Two particles (A and B) move on a straight line and their position (x metres) from the origin O at time t hours is givne by x = sint and sin2t respectively. Write down an interval of time in which both particles are travelling towards the origin with positive velocity.

Could someone please explain to me how on earth to do this question?
Sorry to be slow in answering - I've only just seen your question.

The velocities of the particles are the derivatives of $\displaystyle \sin t$ and $\displaystyle \sin 2t$; i.e. $\displaystyle \cos t$ and $\displaystyle 2\cos 2t$ respectively.

If they are both moving towards the origin with positive velocity, then, for each particle:

• the velocity is positive;

• the displacement is negative (because they are moving towards O).

So, sketch on a single diagram the graphs of $\displaystyle \sin t, \sin 2t, \cos t, 2\cos 2t$, and find an interval for which:

• $\displaystyle \sin t <0, \sin 2t < 0$

• $\displaystyle \cos t > 0, 2\cos 2t > 0$

Can you do it now?