He did gloss over it, but odd cos and even sin is obvious as soon as you define signed angles (which and lengths (which he forgot to mention).
Sin(t) clearly has the same sign as t. (That's why it's called "sin" ;-) )
Sin(t) clearly has the same sign as t. (That's why it's called "sin" ;-) )
He uses the angle addition formulas to derive the Pythagorean theorem, but this derivation only works because he predefined sine and cosine as odd and even functions, which hasn’t been proven