Skip to main content
Workforce LibreTexts

1.5: Trigonometry Functions

  • Page ID
    2635
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    \( \newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\)

    ( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\id}{\mathrm{id}}\)

    \( \newcommand{\Span}{\mathrm{span}}\)

    \( \newcommand{\kernel}{\mathrm{null}\,}\)

    \( \newcommand{\range}{\mathrm{range}\,}\)

    \( \newcommand{\RealPart}{\mathrm{Re}}\)

    \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\)

    \( \newcommand{\Argument}{\mathrm{Arg}}\)

    \( \newcommand{\norm}[1]{\| #1 \|}\)

    \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\)

    \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\AA}{\unicode[.8,0]{x212B}}\)

    \( \newcommand{\vectorA}[1]{\vec{#1}}      % arrow\)

    \( \newcommand{\vectorAt}[1]{\vec{\text{#1}}}      % arrow\)

    \( \newcommand{\vectorB}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vectorC}[1]{\textbf{#1}} \)

    \( \newcommand{\vectorD}[1]{\overrightarrow{#1}} \)

    \( \newcommand{\vectorDt}[1]{\overrightarrow{\text{#1}}} \)

    \( \newcommand{\vectE}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{\mathbf {#1}}}} \)

    \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

    \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)

    When determining the designate angle we can use different ratios of sides.

    • We can use a ratio of the opposite to the hypotenuse.
    • We can use a ratio of the adjacent to the hypotenuse.
    • We can use a ration of the opposite to the adjacent.

    Each ratio has a trigonometric function that helps turn the ratio into an angle. They are:

    • sin θ = opposite/hypotenuse
    • cos θ = adjacent/hypotenuse
    • tan θ = opposite/adjacent

    One way of remembering the ratios are these mnemonics:

    • SOH – Sine is opposite/ hypotenuse
    • CAH – Cosine is adjacent/hypotenuse
    • TOA – Tangent is opposite/ adjacent

    By the way,

    • sin is short for sine
    • cos is short for cosine
    • tan is short for tangent

    Video!

    This video walks through how to determine the angle of a right triangle when you have two sides.

    hqdefault-1.jpg

    A YouTube element has been excluded from this version of the text. You can view it online here: https://pressbooks.bccampus.ca/trigf...tricians/?p=34


    This page titled 1.5: Trigonometry Functions is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by Chad Flinn (BC Campus) via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.