layout | title | categories | enable_mathjax |
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Polar Formulas |
info, precalc |
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r is directed distance
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θ is angle
Generally, equations with
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The same as
$$x^{2} + y^{2} = a^2$$ -
Center at the origin
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Radius of a
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Radius of
$$\frac{a}{2}$$ -
a dictates how far up or down the top/bottom of the circle is
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Radius of
$$\frac{a}{2}$$ -
a dictates how far left or right the edge of the circle is
If...
a = b → Cardioid ♥
a < b → Inner loop
a > b and
a > b and
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If b is odd there are b petals, but if b is even there are 2b petals.
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Each petal is a units long.
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The period of these graphs is always π.
Each petal is of length
- Symmetrical to
$$\theta = \frac{\pi}{4}$$ (the same as y = x)
- Symmetrical to x-axis