[Math] Using the Chain Rule to prove trig derivatives

algebra-precalculuscalculusderivativestrigonometry

I'm having trouble with this problem, I'm not sure how to tackle it and I was wondering if somebody could set me on the right path. The problem is as follows:

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

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

Thanks!

Best Answer

Hint:

$$\frac{d}{d \theta}\sin(\theta^{\circ}) = \frac{d}{d\theta} \sin\left(\frac{\pi}{180^{\circ}} \cdot \theta^{\circ}\right).$$

Now, can you apply the chain rule?