Skip to main content
Mathematics LibreTexts

7.8.1: Key Terms

  • Page ID
    116136
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \)

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

    Key Terms

    damped harmonic motion
    oscillating motion that resembles periodic motion and simple harmonic motion, except that the graph is affected by a damping factor, an energy dissipating influence on the motion, such as friction
    double-angle formulas
    identities derived from the sum formulas for sine, cosine, and tangent in which the angles are equal
    even-odd identities
    set of equations involving trigonometric functions such that if f( x )=f( x ), f( x )=f( x ), the identity is odd, and if f( x )=f( x ), f( x )=f( x ), the identity is even
    half-angle formulas
    identities derived from the reduction formulas and used to determine half-angle values of trigonometric functions
    product-to-sum formula
    a trigonometric identity that allows the writing of a product of trigonometric functions as a sum or difference of trigonometric functions
    Pythagorean identities
    set of equations involving trigonometric functions based on the right triangle properties
    quotient identities
    pair of identities based on the fact that tangent is the ratio of sine and cosine, and cotangent is the ratio of cosine and sine
    reciprocal identities
    set of equations involving the reciprocals of basic trigonometric definitions
    reduction formulas
    identities derived from the double-angle formulas and used to reduce the power of a trigonometric function
    simple harmonic motion
    a repetitive motion that can be modeled by periodic sinusoidal oscillation
    sum-to-product formula
    a trigonometric identity that allows, by using substitution, the writing of a sum of trigonometric functions as a product of trigonometric functions

    7.8.1: Key Terms is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

    • Was this article helpful?