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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*}