SOLUTION: Test the symmetry (with respect to the polar axis, to the pole, and to the vertical line θ=π/2) and sketch the graph of the polar equation r = 3+2sin(θ) (4 points)

Question 1205368: Test the symmetry (with respect to the polar axis, to the pole, and to the vertical line θ=π/2) and sketch the graph of the polar equation r = 3+2sin(θ) (4 points)

Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
the polar equation

the -axis - called the axis
the line (-axis)
the pole is origin

test for symmetry about polar-axis: replace with and see is unchanged
....since , we have
=>not same as what we started with, is changed; so, no symmetry about -axis or the polar axis

test the line ( -axis): replace () with () and see is unchanged
...since
=> same as what we started with, is ; so, there is symmetry about -axis or the the line

test the pole is origin (° rotation), replace with and see is unchanged
. = > obviously is changed, so no symmetry abut pole (origin)

graph it:

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