Problem 87E

87. Use the Chain Rule to show that if $\theta$ is measured in degrees, then

$$\frac{d}{d \theta}(\sin \theta)=\frac{\pi}{180} \cos \theta$$

(This gives one reason for the convention that radian measure is always used when dealing with trigonometric functions in calculus: the differentiation formulas would not be as simple if we used degree measure.)