Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5 - Page 142: 59

$sin(x)$

Step 1. $\frac{d}{dx}(cos(x))=-sin(x)$ Step 2. $\frac{d^2}{dx^2}(cos(x))=-cos(x)$ Step 3. $\frac{d^3}{dx^3}(cos(x))=sin(x)$ Step 4. $\frac{d^4}{dx^4}(cos(x))=cos(x)$ .... Step 5. The derivative will repeat every fourth item, since $999=1000-1=4(250)-1=4(249)+3$, we have $\frac{d^{999}}{dx^{999}}(cos(x))=sin(x)$ (results from step 3)