# Math Help - Finding trig values using a series

1. ## Finding trig values using a series

Hello, 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...

2. 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,

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 . . .