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Consider a particle following the parametric equations

below

\(below \begin{align*} x &= 1 + \sin (\pi t),\\ y &= 3 \sin (\pi t). \end{align*}\)

Find the first four positive times t when this particle visits the point (3/2, 3/2) and list them in increasing order.

 May 8, 2021
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x  =  1  +  sin (pi * t)

 

3/2  =1 + sin (pi * t)

 

3/2  -1  = sin (pi * t)

 

1/2  =  sin (pi * t)

 

Note  that   for  the  correct  values of t ,  y  must  also  = 3/2....so.. the  sine  must be  positive  in both cases.....so...t  must produce  a first  quadrant  angle  in both cases

 

This  happens  when     t   =   (1/6)     t   =  (1/6) + 2    t =  (1/6) + 4    t  =(1/6)  + 8

 

So

 

t  =   (1/6)   ,  (13/6)   , ( 25/6)   and  (37/6)

 

 

cool cool cool

 May 8, 2021
edited by CPhill  May 8, 2021

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