find the radius of curvature of the limacon r= b cos thita at any point.
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Step-by-step explanation:
Explanation:
graph{x^2+y^2-sqrt(x^2+y^2)-2y=0 [-10, 10, -5, 5]}
If you agree that the polar coordinate r is length (modulus ) of a
vector and accordingly r = the positive
√
x
2
+
y
2
, limacons
r
=
a
+
b
cos
(
θ
−
α
)
have dimples but not inner loops.
For examples, r=2+cos theta and r = 1-sin theta#
have nodes ( points with two distinct tangent directions ) that create
dimples
Unless you allow negative values for r,
the question of having inner loop is ruled out.
The first limacon is for
r
=
1
−
sin
θ
The ones below are for
r
=
2
+
cos
θ
and
r
=
1
−
1.5
sin
θ
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