Differentiate the law of Cosine

ryank614
Messages
8
Reaction score
0
It is a simple math question, but I am stuck.

The law of cosines is

R^2=h^2 + r^2 - 2 h r cos (theta). Theta is of course the angle facing R.

To differentiate, I first set

r^2 - 2hr cos\Theta+ (h^2-R^2) = 0

2 r \dot{}r - 2 h cos\Theta \dot{}r + (h^2-R^2) = 0.

Is there any way to put h^2-R^2 in terms of \dot{}\theta or d\theta/dt
 
Physics news on Phys.org
Arr, nevermind. I got it.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top