I am playing with the equation by which the Dottie Number is calculated:

cox(x) - x = 0

x = 0.739085133215160641655312087673873404013411758900 757464965680...

This is the so-called Dottie Number.

I am wondering if there is ANY relation between the x-value calculated according to the equation above, and the x_{1}-value calculated according to the following equation:

cos(x_{1}/2) - x_{1}= 0

AFAIK, both equations produce unique numbers. However, I can't think of any relationship between the results. Am I overlooking some property by which a relationship between x and x_{1}could be defined?