Part 1/5:

Understanding the Derivative of Cosine: A Step-by-Step Proof

In the world of calculus, derivatives are foundational concepts that help us understand the behavior of functions. In this article, we will discuss the derivative of the cosine function, providing a detailed proof utilizing the definition of a derivative. This exploration is complementary to previous discussions on the sine function’s derivative.

Graphing Cosine

To begin, let’s visualize the graph of the cosine function. The cosine function, denoted as (f(x) = \cos(x)), oscillates between a maximum value of 1 and a minimum value of -1.

As we examine its graph:

At its peak (maximum), the slope is 0. This peak occurs at points such as (x = 0, 2\pi, 4\pi), etc.