cunning narwhal
like sine and cosine law?
#Have you ever struggled with trigonometry?
rose parcel
For me, I’ve never really thought of the intuition behind trig but it did bother me a bit not completely understanding it, but when I learned about complex numbers it all clicked for me, similitudes and rotations via multiplication of complex numbers and polar coordinates gave me insight about how angles and trigonometry works in my opinion but that’s just me
Also rotational matrices can give a bit of insight ( which is a bit like complex numbers)
Like, the formulas for cos(a+b) and sin(a+b) where do they come from? there are many ways to find the formulas but one intuitive way to do it is via rotations what is cos(a+b) and sin(a+b)? Well they are the coordinates of the vector of the rotation of angle a+b and length 1 ( so you can look at the trig circle ) so if you take the vector v=(1,0) you want to rotate it by a degrees then you can multiply v by the rotational matrice of angle a+b but you can also say that it’s by the rotational matrice of angle a then that of b so first multiplying by the angle a you get the vector (cos(a),sin(a)) then you want another rotation of angle b so remultiplying you get
(cos(a)cos(b)-sin(a)sin(b),sin(a)cos(b)+sin(b)cos(a))
So exactly what is needed
The proof is the same with complex numbers but using a different mathematical Language which is matrices ( both being extremely linked because complex number multiplication can be represented with matrices so it’s basically the same proof)
Sorry for being a yappertron-3000 I need to stop overwriting
sour echo
You may enjoy first studying the history of the science throughthe classic mathematical works. You should be able to pick up trig in an enjoyable manner by reading Euclid, Archimedes, Ptolemy, Copernicus, Kepler and Descartes because it's roots are beginning to form in those periods. The whole historical development may spark your enthusiasm.
hard linden