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.
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)