Posted by dreidel on Wednesday, December 18, 2013 at 10:34pm.
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, Thursday, December 19, 2013 at 12:25am
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, Thursday, December 19, 2013 at 6:05pm
Thx!
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