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)
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-> 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)
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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)
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)