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.

Related questions
See all questions in Converting Equations from Polar to Rectangular
Impact of this question
17417 views around the world
You can reuse this answer
Creative Commons License