Skip to main content
\(\require{cancel}\)
Physics LibreTexts

10.4: Mathematical Formulas - Trigonometry

  • Page ID
    24319
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    \[e ^ { j \theta } = \cos \theta + j \sin \theta\]

    \[\cos \theta = \frac { 1 } { 2 } \left( e ^ { j \theta } + e ^ { - j \theta } \right)\]

    \[\sin \theta = \frac { 1 } { j 2 } \left( e ^ { j \theta } - e ^ { - j \theta } \right)\]

    \[\cos ^ { 2 } \theta = \frac { 1 } { 2 } + \frac { 1 } { 2 } \cos 2 \theta\]

    \[\sin ^ { 2 } \theta = \frac { 1 } { 2 } - \frac { 1 } { 2 } \cos 2 \theta\]

    Contributors and Attributions


    10.4: Mathematical Formulas - Trigonometry is shared under a CC BY-SA 4.0 license and was authored, remixed, and/or curated by Steven W. Ellingson.

    • Was this article helpful?