How do you graph #r=3/sin(theta)#?

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Answer 1 · 2017-08-02T21:22:49

The easiest way to graph the equation is to observe that it converts to #y = 3# using the following steps:

#r = 3/sin(theta)#

#rsin(theta)=3#

#y = 3#

This is a horizontal line at #y = 3#

If you want to stay with polar coordinate system, avoid division by 0 and a negative radius by adding the restriction:

#r = 3/sin(theta); 0 < theta < pi#

Then start plotting points:

#(3,pi/2)#, #(6,pi/6)#, #(6,5pi/6)#

If you connect these 3 points, you will see that it is a horizontal straight line segment.