Hello, rman12011!

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! + . . .

wherexis 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 . . .