![]() Recall that for a function f ( x ), f ( x ) ,ĭ d x sin x = lim h → 0 sin ( x + h ) − sin x h Apply the definition of the derivative. We begin our exploration of the derivative for the sine function by using the formula to make a reasonable guess at its derivative. Derivatives of the Sine and Cosine Functions Being able to calculate the derivatives of the sine and cosine functions will enable us to find the velocity and acceleration of simple harmonic motion. We begin with the derivatives of the sine and cosine functions and then use them to obtain formulas for the derivatives of the remaining four trigonometric functions. ![]() In this section we expand our knowledge of derivative formulas to include derivatives of these and other trigonometric functions. Simple harmonic motion can be described by using either sine or cosine functions. One of the most important types of motion in physics is simple harmonic motion, which is associated with such systems as an object with mass oscillating on a spring. 3.5.3 Calculate the higher-order derivatives of the sine and cosine.3.5.2 Find the derivatives of the standard trigonometric functions.3.5.1 Find the derivatives of the sine and cosine function.
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