+---
+geometry: margin=1.9cm
+columns: 2
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+author: Andrew Lorimer
+---
+
# Circular functions
Period of $a\sin(bx)$ is ${2\pi} \over b$
- **Turning points** at $\theta = {{(2n + 1)\pi} \over 2} \> \vert \> n \in \mathbb{Z}$
- **Asymptotes** at $\theta = n\pi \> \vert \> n \in \mathbb{Z}$
-
### Secant
-!()[graphics/sec.png]
+![](graphics/sec.png)
$$\operatorname{sec} \theta = {1 \over \cos \theta} \> \vert \> \cos \theta \ne 0$$
- **Turning points** at $\theta = n\pi \> \vert \> n \in \mathbb{Z}$
- **Asymptotes** at $\theta = {{(2n + 1) \pi} \over 2} \> \vert \> n \in \mathbb{Z}$
-
### Cotangent
-!()[graphics/cot.png]
+![](graphics/cot.png)
$$\operatorname{cot} \theta = {{\cos \theta} \over {\sin \theta}} \> \vert \> \sin \theta \ne 0$$
## Double angle formulas
\begin{equation}\begin{split}
- \cos 2x = \cos^2 x = \sin^2 x
+ \cos 2x &= \cos^2 x - \sin^2 x \\
+ & = 1 - 2\sin^2 x \\
+ & = 2 \cos^2 x -1
\end{split}\end{equation}
$$\sin 2x = 2 \sin x \cos x$$