Given x = 2 cot t and #y = 2 sin^2 t# for #0<t<= pi/2# how do you find the cartesian equation for this curve and state the domain?

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Answer 1 · 2016-07-16T14:07:18

# y = 8/(x^2 + 4) #

#cot t = x/2, cot^2 t = x^2/4#

#sin^2 t = y/2, csc^2 t = 2/y#

using #cot^2 + 1 = csc^2# we have

#x^2/4 + 1 = 2/y#

#y/2 = 1/(x^2/4 + 1) = 4/(x^2 + 4) #

# y = 8/(x^2 + 4) #

the domain is #x in mathcal(R)#