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)

Algebra ->  Quadratic-relations-and-conic-sections -> 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)       Log On


   



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) About Me  (Show Source):
You can put this solution on YOUR website!
the polar equation r+=+3%2B2sin%28theta%29

the x -axis - called the polar axis
the line theta=pi%2F2 (y-axis)
the pole is origin

test for symmetry about polar-axis: replace theta with -theta and see is r+unchanged
r+=+3%2B2sin%28-theta%29....since sin%28-theta%29=-sin%28theta%29, we have
r+=+3-2sin%28theta%29 =>not same as what we started with, r is changed; so, no symmetry about x-axis or the polar axis

test the line theta=pi%2F2 ( y-axis): replace (theta) with (pi-theta) and see is r unchanged
r+=+3%2B2sin%28pi-theta%29...since sin%28pi-theta%29=sin%28theta%29
r+=+3%2B2sin%28theta%29=> same as what we started with, r is not+changed; so, there is symmetry about y-axis or the the line theta=pi%2F2

test the pole is origin (180° rotation), replace r with -r and see is r unchanged
.-r+=+3%2B2sin%28theta%29 = > obviously r is changed, so no symmetry abut pole (origin)

graph it:
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