In mathematical terms, the derivative of sine function, often denoted as sin'(x) or d/dx[ sin(x) ], is cosine(x). Key to understanding this derivative is the knowledge that differentiation of trigonometric functions transforms them into other trigonometric functions. More specifically, sine is a periodic function that measures the distance on a circle, and cosine function measures the adjacent distance on a circle. As a result, the rate of change of the sine function can be expressed in terms of cosine function.

The derivative of the sine function is simply the cosine function. This holds true as a general rule in basic derivative calculus. If you’ve ever studied trigonometric functions, you would understand that sine and cosine are very much interconnected. In essence, they are measurements at different stages on a circle. As such, when you differentiate sine, you actually get the cosine function.