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A.7: Trigonometry — Simple Identities

  • Page ID
    91823
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    • 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*}


    This page titled A.7: Trigonometry — Simple Identities is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Joel Feldman, Andrew Rechnitzer and Elyse Yeager via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.