How do you graph #r=-6sintheta#?

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Answer 1 · 2016-10-01T01:29:20

It is a circle with center at (0, -3) and radius, 3:
#x^2 + (y - -3)^2 = 3^2#

Multiply both sides by r:

#r^2 = -6rsin(theta)#

Substitute #x^2 + y^2# for r and y for #rsin(theta)#

#x^2 + y^2 = -6y #

#x^2 + y^2 + 6y = 0#

#x^2 + y^2 + 6y + 9 = 9#

#x^2 + (y + 3)^2 = 3^2#

#x^2 + (y - -3)^2 = 3^2#