My calculus teacher brought up something very interesting concerning
the ability to figure out the value of a trig function through a series.
However she didn't go on to really teach about it,
I am curious about this and was wondering if anyone knew about this...
When you get into Infinite Series, you learn two fascinating series:
. . sin x .= .x - (x^3)/3! + (x^5)/5! - (x^7)/7! + . . .
. . cos x .= .1 - (x^2)/2! + (x^4)/4! - (x^6)/6! + . . .
where x is measured in radians.
Sines and cosines come from some right triangle, yet with Infinite Series:
. . the sine has odd powers and odd factorials (and alternating signs)
. . the cosines has even powers and and even factorials (and alternating signs).
I think it's a remarkable pattern . . .