I'm Billy,
student in secondary5

Question:
The parametric equation of cycloid is given:
x=r(t-sint)
y=r(1-cost)

How to eliminate t?

Billy

You can solve the second equation for cost, cost = 1 - y/r and then t is the inverse cosine of 1 - y/r. Substitute this into the first equation for the first t and then express sint using the fact that sin²t + cos²t = 1.

The parametric form is much easier to work with.