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Section A.7 Trigonometry — Simple Identities
Periodicity
\begin{align*}
\sin(\theta+2\pi) &= \sin(\theta) &
\cos(\theta+2\pi) &= \cos(\theta)
\end{align*}
Reflection
\begin{align*}
\sin(-\theta)&=-\sin(\theta) & \cos(-\theta) &=\cos(\theta)
\end{align*}
Reflection around
\(\pi/4\)
\begin{align*}
\sin\left(\tfrac{\pi}{2}-\theta\right)&=\cos\theta &
\cos\left(\tfrac{\pi}{2}-\theta\right)&=\sin\theta
\end{align*}
Reflection around
\(\pi/2\)
\begin{align*}
\sin\left(\pi-\theta\right)&=\sin\theta &
\cos\left(\pi-\theta\right)&=-\cos\theta
\end{align*}
Rotation by
\(\pi\)
\begin{align*}
\sin\left(\theta+\pi\right)&=-\sin\theta &
\cos\left(\theta+\pi\right)&=-\cos\theta
\end{align*}
Pythagoras
\begin{align*}
\sin^2\theta + \cos^2 \theta &=1
\end{align*}
