Math tools and more.
r is directed distance
θ is angle
\(x^{2} + y^{2} = r^{2}\), \(x = r\cos\theta\), \(y = r\sin\theta\)
\(\cos\theta = \frac{x}{r}\), \(\sin\theta = \frac{y}{r}\), \(\tan\theta = \frac{y}{x}\)
Generally, equations with \(\sin\) are symmetric to the y-axis (except for lemniscates), while equations with \(\cos\) are symmetric to the x-axis.
\(r = a\sec\theta\) is the same as \(x = a\)(vertical line)
\(r = a\csc\theta\) is the same as \(y = a\)(horizontal line)
\(r = a\)
The same as \(x^{2} + y^{2} = a^2\)
Center at the origin
Radius of a
\(r = a\sin\theta\) or \(r = - a\sin\theta\)
Radius of \(\frac{a}{2}\)
a dictates how far up or down the top/bottom of the circle is
\(r = a\cos\theta\) or \(r = -a\cos\theta\)
Radius of \(\frac{a}{2}\)
a dictates how far left or right the edge of the circle is
\(r = a \pm b\sinθ\) or \(r = a \pm b\cosθ\)
If…
a = b → Cardioid ♥
a < b → Inner loop
a > b and \(\frac{a}{b} < 2\) → Dimpled circle
a > b and \(\frac{a}{b} \geq 2\) → Flat circle
\(r = a\ sin\ b\theta\) or \(r = a\ cos\ b\theta\)
If b is odd there are b petals, but if b is even there are 2b petals.
Each petal is of length \(a\).
\(r^{2} = a^{2}sin2\theta\)
\(r^{2} = a^{2}cos2\theta\)
Right-click or long press any of the math, then click Math Settings → Scale All Math... Type a number such as 125% or 200%.