How do you convert #r=tan(theta)sec(theta)# into cartesian form?

1 Answer
Roella W.
Jan 8, 2016

By substitution #y = x^2#

Explanation:

First convert the expression into terms of #cos(theta)# and #sin(theta)#
#r = sin(theta)/cos(theta) *1/cos(theta)#
#rcos^2(theta) = sin(theta)#
Now the normal substitutions are #x=rcos(theta)# and #y=rsin(theta)#
#:. sin(theta) = y/r# and #cos(theta) = x/r#

Substituting these values into the expression above gives
#r*(x/r)^2 = y/r#
#cancel(r)*x^2/r^cancel(2) = y/r#
#x^2 = r*y/r = y#
#:.y = x^2#

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