How do you convert #r=-3sectheta# into rectangular equations?

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Answer 1 · 2016-07-15T06:00:43

#x = -3#

Knowing that #x = r cos(theta)# and #y = r sin(theta)#, we can start off by rewriting our polar equation:

#r = -3sec(theta) = -3 * (1)/(cos(theta))#, so then

#r = -3/cos(theta)#

Multiplying both sides by #cos(theta)# gives us

#r cos(theta) = -3#

Substituting #x# for #r cos(theta)#, since #x = rcos(theta)# we get

#x = -3#