Derivatives of Sine and Cosine

The derivatives of the sine and cosine functions are:

In both formulas θ is measured in radians. We can see intuitively why these are the derivatives in Figure 2.5.5.

In the triangle under the infinitesimal microscope.

Notice that cos θ decreases, and Δ(cos θ) is negative in the figure, so the derivative of cos θ is -sin θ instead of just sin θ.

Using the rules of differentiation we can find other derivatives.