Posted by
dreidel on
.
To what interval I must we restrict the parameter t if the graph of the parametric equations
x=t+1
y = 2t^2 +1
for t in the set I
is identical to the graph of the parametric equations
x = 1+ sin s
y = 2 cos(2s)
for s in [0,pi)?

precalculus 
Steve,
it appears we need
1+t = 1+sin s,so
t = sin s
t must be in [0,1] if s is in [0,pi)
also,
2t^2+1 = 2cos(2s)
2t^2+1 = 2  (12sin^2 s)
2t^2+1 = 2sin^2 s + 1
same domain.

precalculus 
dreidel,
Thx!