How do you convert #r = 4csc(x)# into cartesian form?

1 Answer
mason m
Jan 24, 2017

Assuming the equation was #r=4csctheta#, the rectangular form is #y=4#.

Explanation:

(Assuming that the equation you meant is #r=4csctheta#, since polar equations use #r# and #theta#.)

When converting from polar to rectangular, it's important to know that:

  • #x=rcostheta#
  • #y=rsintheta#

The equation can be rewritten using #csctheta=1/sintheta# and then multiplying both sides by #sintheta#:

#r=4csctheta" "=>" "r=4/sintheta" "=>" "rsintheta=4#

With the identity from before:

#y=4#

which is a horizontal line.

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