7: Derivatives of Trigonometric Functions
- Page ID
- 36879
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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.