7: Derivatives of Trigonometric Functions
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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:
[sint]′=cost[cost]′=−sint
The derivative equation
y′′(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)=Acost+Bsint
where A=y(0) and B=y′(0) are constants.