Good morning, I currently starting my journey to study mathematics more seriously. I'd like to focus now in trigonometry. I know just about all the trigonometric identities half angle, double angles, sum difference, inverse-functions, Pythagorean and such. I however, want a book that does not teach me how to compute (which I know). I'd love a book with geometric interpretations and proofs as well as algebraic.
For example:
What does it mean to have sin($3\theta$)... Do I have three triangles?...
what does it mean to have sin($\theta/2$)...Do I cut my triangle in half?...
What is the proof for summation of double or even triple angles! how does it make geometric sense... where is its proof...
etc..
I only want theory with the intuition behind things. Unfortunately when I try to search up books for trigonometry they only focus on blindly applying a property that they don't fully define.
Thank you for any tips and ideas.
