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7: Derivatives of Trigonometric Functions

  • Page ID
    36879
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    Where are we going?

    The trigonometric functions, sine and cosine, are useful for describing periodic variation in mechanical and biological systems. The sine and cosine functions and their derivatives are interrelated:

    \[\begin{aligned}
    &{[\sin t]^{\prime}=\cos t} \\
    &{[\cos t]^{\prime}=-\sin t}
    \end{aligned}\]

    The derivative equation

    \[y^{\prime \prime}(t)+y(t)=0\]

    is basic to mathematical models of oscillating processes, and every solution to this equation can be written in the form

    \[y(t)=A \cos t+B \sin t\]

    where \(A = y(0)\) and \(B = y ^{\prime} (0)\) are constants.

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    This page titled 7: Derivatives of Trigonometric Functions is shared under a CC BY-NC-ND license and was authored, remixed, and/or curated by James L. Cornette & Ralph A. Ackerman.

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