Convert the the polar equation # x=cos theta # and # y = sec theta # where #theta in [0,pi/2]# to cartesian coordinates?

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Answer 1 · 2017-06-30T21:19:58

# y = 1/x# where #x in [0,1]#

We have:

# x=cos theta # where #theta in [0,pi/2]#
# y = sec theta #

First let us graph the curve for validation purposes:
enter image source here

So to convert to rectangular coordinates we can use:

# y = sec theta => y = 1/cos theta #
# :. y = 1/x #

If we sketch this graph we have:
enter image source here

So we have the correct graph but an incorrect domain.

# theta = 0 \ \ => x=cos0 = 1 #
# theta = pi/2 => x=cos(pi/2) = 0 #

And if we ow restrict the domain of # y = 1/x# to #x in [0,1]# we have:
enter image source here