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# parametric equations

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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.

Oct 11, 2022

#1
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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.

$${25\over18}, {61\over18}, {97\over18}, {133\over18}$$

Oct 11, 2022