How do you graph # r = 4sin(theta)#?

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Answer 1 · 2016-02-23T22:32:13

The graph belongs to the conic family called circle. Assign several values for #theta# then compute corresponding #r# then plot the graph

The given #r=4sin theta# is equivalent to

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

and by completing the square

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

also using the "center-radius form#

#(x-h)^2+(y-k)^2=r^2#
#(x-0)^2+(y-2)^2=2^2#
center #(h, k)=(0, 2)#

with radius #r=2#

now, you are ready to graph

kindly see the graph below
graph{x^2+y^2=4y[-10,10,-5,5]}

You may also use #r=4 sin theta# right away by assigning values for #theta# and noting all #(r, theta)# coordinates.

God bless you...