Consider a particle following the parametric equations

x = 1 + sin(pi*t)

y = 3*sin(3*pi*t)

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

Guest Oct 11, 2022

#1**+2 **

The x coordinate can never reach the value of 3/2, but the y value can.

After some calculations, you'll see that when t = 25/18, it reaches 3/2. Then add 2 every time, so the second time it reaches will be at 61/18, then 97/18 then 133/18.

\({25\over18}, {61\over18}, {97\over18}, {133\over18}\)

proyaop Oct 11, 2022