The sun did not shine.
It was too wet to play (ride).
So I sat in the house
All that cold, cold, wet day.:(
Hmm - the lengths rain-induced boredom will drive me to! I think we basically agree. I just get a bit OCD when it comes to accuracy in mathematics and physics. I guess it is my job to care about such things!:o
I think we agree that there are different tools and that each has benefits used in certain applications and I have no discomfort in understanding or applying any of them in the circumstances that fit. I have certainly not meant to imply otherwise.
A wise(a$$?) engineer who sits near me at work and comes out with sage sayings is fond of saying "An engineer is somebody who is trained to do with $2 what anybody could do with $100." I have been conditioned therefore to select the method of least complexity (needing fewer terms) and greatest efficiency to get the job done (answer the OP's question).
Your choice to stretch the mind further with the choice of a different tool is I'm sure the result of a different set of conditioning in your makeup! I'm sure between us at least we've improved the world's statistics on mathematical illiteracy just a little?:D

