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Homework Statement
Eliminate the parameter to find the Cartesian equation of the curve.
Problem #1:
x = sin t, y = csc t, 0 < t < ∏ / 2
Problem #2:
x = sin θ, y = cos 2θ
Homework Equations
What's shown above is what's listed in the book. However, the authors felt compelled to include the domain (for the the second problem) and range (for the first problem) in the answers section in the back of the book which are as follows:
Problem #1:
{y|y > 1}
Problem #2:
{x|- 1 ≤ x ≤ 1}
I'm not sure how they got that (as it has been a year since I finished precal) and I don't think my professor requires me to know how to get the domain and range for these problems, but I'd like to know how just in case I ever come across something like this again.
The Attempt at a Solution
If it makes any difference, here are the Cartesian equations (and the work it took to get them):
Problem #1:
x = sin t
y = csc t
y = 1 / sin t
y = 1 / x
Problem #2:
x = sin θ
y = cos 2θ
y = cos θ^2 - sin θ^2
y = 1 - 2sin θ^2
y = 1 - 2x^2