How do you graph #r=-2sintheta#?

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Answer 1 · 2016-10-14T19:02:10

The way that you graph this is, set your compass to a radius of 1, put the center point at #(0, -1)#, and draw a circle.

Multiply both sides by r:

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

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

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

Write #x^2 as (x - 0)^2#:

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

Add #2y + k^2# to both sides:

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

Using the pattern #(y - k)^2 = x^2 - 2ky + k^2# we observe that we can use the 2y term to find the value of #k and k^2#:

#-2ky = 2y#

#k = -1 and k^2 = 1#

Substitute this into the equation:

#(x - 0)^2 + y^2 + 2y + 1= 1#

This means y terms on the left side can be written as #(y - -1)^2#:

#(x - 0)^2 + (y - -1)^2 = 1^2#

The way that you graph this is, set your compass to a radius of 1, put the center point at #(0, -1)#, and draw a circle.