Would you agree that that amount of time indicates lack of mastery? And that it’s partly lack of mastery of trig concepts, rather than only of writing?
BTW, placing a low value on writing is a systemic error in math and physics related to anti-conceptual attitudes. Writing in a language like English is humanity’s best general tool for dealing with concepts/ideas. Being able to explain concepts in words is a big part of how people learn them, think about and discuss them, improve them, etc. It also helps with remembering without memorizing.
[Insert picture here]
What’s the reason for omitting pictures? That also seems like it indicates lack of relevant mastery. In other words, you find something hard or burdensome about including the pictures. The process is not easy/intuitive/automatic for you. That seems problematic because working with diagrams on computers is a relevant useful skill for your fields. (Related, I noticed you didn’t use any MathJax in this post or IIRC previously, which could indicate a lack of mastery of LaTeX, which also seems relevant to your fields.)
Also, do you agree that trig is a relevant building block to your field, and something you should be good at?
The big picture is that, while you know some stuff about how it works, I think the concepts and writing are both kinda a mess. It’s not well-organized, streamlined knowledge. It has “code smells” if you know that term. This is different than wrong and is compatible with doing the calculations correctly for tests.
I want to start with the above, not explain this part more yet, but I didn’t want to leave out an overall comment entirely.