Expert: Sherman D. - 7/31/2006

Question
http://experts.about.com/q/Basic-Math-657/Trig-Pointgs.htm

I read this earlier and tried to apply it to my homework question
evaulate: cos (-(8*pi/3)).

my working is this:
(9*pi/3) - (pi/3) = 360 + 180 - 60 (3pi being 1 1/2 revolution (540), and pi/3 60 degree)
=480 - 360 = 120 degree angle.
So
Cos x = -cos(pi - x)
cos (-(8*pi/3))= -cos ((9*pi/3) - (8*pi/3))
=-cos(pi/3)
=-cos 60; since cos 60 = 1/2
-cos 60 = -1/2
is this correct? is my working understandable?

Answer
You must had did it correctly, since that is the right answer, but here is what i would had done.

cos((-8pi)/3)

cos(x - y) = cosxcosy + sinxsiny

cos((pi/3) - ((9pi)/3))
cos((pi/3) - 3pi) = 60 - (360 + 180) = 60 - 540 = -480

cos(-480) = -cos(480) = -cos(360 + 120) = -(cos(360) + cos(120)) = (-1/2)

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the true formula for doing this is

cos(x + y) = cosxcosy - sinxsiny
cos(x - y) = cosxcosy + sinxsiny

http://www.math.com/tables/trig/identities.htm