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Sketching a polar curve
can be tricky.
Some guidelines for plots in polar coordinates are
as follows:
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If polar equation is same when replacing
θ with ˗ θ, then the curve is
symmetric about its
polar axis, the x˗axis.
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If polar equation is
same when r is replaced by ˗
r or when θ
is replaced
by θ + π, then curve is
symmetric about its pole, the origin.
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If polar equation is
same when θ is replaced by
π ˗ θ, then curve is symmetric
about the vertical
line θ = π/2.
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If needed, plot a few
convenient points that are easy to calculate.
i.e. θ = 0, θ = π/4, θ = π/2, etc.
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