Answer
$\frac{d}{d\theta}(sin~\theta) = \frac{\pi}{180}~(cos~\theta)$
Work Step by Step
Let $\theta$ be the angle measured in degrees.
Then the angle measured in radians is $\frac{\pi~\theta}{180}$
We can differentiate the function using radians:
$\frac{d}{d\theta}(sin~\frac{\pi~\theta}{180}) = \frac{\pi}{180}~(cos~\frac{\pi~\theta}{180})$
We can rewrite the equation with the angle in degrees:
$\frac{d}{d\theta}(sin~\theta) = \frac{\pi}{180}~(cos~\theta)$
