# Thread: Prove d/dθ(sinθ) = pie/180cosθ (chain rule)

1. ## Prove d/dθ(sinθ) = pie/180cosθ (chain rule)

Use the Chain Rule to show that if θ is measured in degrees, then:

d/dθ(sinθ) = pie/180cosθ

I could only derive the left side to cosθ, but had no clue what to do with the right side.

2. well then you have:

cosθ = pie / 180cosθ

180cosθ = pie / cosθ

180cos²θ = pie

Basic, erm, also, you know that 180 degrees = pie as well

3. Originally Posted by TsAmE
Use the Chain Rule to show that if θ is measured in degrees, then:

d/dθ(sinθ) = pie/180cosθ

I could only derive the left side to cosθ, but had no clue what to do with the right side.
It is because $\theta ^{\circ} = \frac{\pi}{180} \theta$

By the chain rule (for a constant a): $\frac{d}{d \theta}\, \sin (a \theta) = a\cos(a \theta)$

4. But there was no constant in the question? And wouldnt you only work with the left hand side-d/dθ(sinθ), to get to (pie / 180) * cosθ since you are kind of proving the left hand side? Sorry but I am kind of confused

5. Originally Posted by TsAmE
But there was no constant in the question? And wouldnt you only work with the left hand side-d/dθ(sinθ), to get to (pie / 180) * cosθ since you are kind of proving the left hand side? Sorry but I am kind of confused
You want to manipulate the left side to get the right side

You are given theta in degrees and since $\frac{d}{dx} \sin(x) = \cos(x)
$
only holds in radians then you need to convert degrees to radians.

6. Ok that makes more sense, but by differentiating the LHS, it seems that chain rule wasn't used, and just the trig derivative, yet the question said prove using chain rule. Sorry again if I am asking a dumb question