How to draw graph of #r= 3sintheta+4costheta#?

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Answer 1 · 2018-03-12T08:58:41

Draw a circle with a center at #(2,3/2)# with a radius of #2.5#.

Multiply both sides by #r# to get #r^2=3rsintheta+4rcostheta#

#r^2=x^2+y^2#
#3rsintheta=3y#
#4rcostheta=4x#

#x^2+y^2=3y+4x#

#x^2-4x+y^2-3y=0#

#(x-2)^2-4+(y-3/2)^2-9/4=0#

#(x-2)^2+(y-3/2)^2=4+9/4=25/4#

Draw a circle with a center at #(2,3/2)# with a radius of #2.5#.