When I took Trigonometry in high school, it was all about memorizing a bunch of stuff and I did horribly. When I took it in college, the professor taught us how to derive everything based on the Unit Circle. It just clicked. I ended up doing so well in that class that the professor got me to change my major to mathematics and got me a scholarship too.
I ctrl-f'ed for this one. First exposure was SOHCAHTOA and memorization without building intuition. I struggled and had no real understanding. Two years later a physics teacher draws a unit circle with sine and cosine marked out as an incidental explanation for something else, and 2 years of frustration suddenly clicked. Gave me huge appreciation for the power of a good explanation.
