First, students will learn how to prove the derivative rules for \(\sin\) and \(\cos,\) which are:

$$\begin{align} & \dfrac{d}{dx}\sin x = \cos x \\[1em] & \dfrac{d}{dx}\cos x = -\sin x \end{align}$$Watch these Mathispower4u videos:

Next, students will learn how to prove the derivative rules for \(\tan,\) \(\sec,\) \(\csc,\) and \(\cot,\) which are:

$$\begin{align} & \dfrac{d}{dx}(\tan x) = \sec^2 x \\[1em] & \dfrac{d}{dx}(\cot x) = -\csc^2 x \\[1em] & \dfrac{d}{dx}(\sec x) = \sec x\tan x \\[1em] & \dfrac{d}{dx}(\csc x) = -\csc x\cot x \end{align}$$Watch these Khan Academy videos:

After that, students will see a visual proof of the derivative rule for \(\sin.\)

Visual Calculus: Derivative of sin(θ) is cos(θ) by Think Twice

Conclude by giving your students these challenges:

- Fruit in a Bowl by NRICH
- Two Ladders by NRICH
- The Spider and the Fly by NRICH
- 2006 AMC 8, Problem 17
- 2007 AMC 8, Problem 20