# Re: pre-calc-is this the right way????

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Posted by T.Gracken on October 23, 2002 at 19:03:46:

In Reply to: pre-calc-is this the right way???? posted by Jacquie on October 21, 2002 at 18:17:29:

: find exact value of cos 11pi/12
: i used the double-angle formula for cos
: sq. root of (1 + cos 11pi/12)/2
: sq. root of(1+cos(8pi/12 + 3pi/12))/2
: sq. root of(1+cos(2pi/3 + pi/4))/2
: sq. root of(1+(-1/2)+ (sq.root of2/2))/2
: sq. root of(2/2+sq. root of2-1/2/2
: sq.root of(sq. root of 2 +1/2)/2
: but i dont know how to further reduce this???

Another way to approach this is

consider that 11pi/12 = 3pi/12 + 8pi/12

which (reduced) gives 11pi/12 = pi/4 + 2pi/3

Now use sum of angles (cosine) identity

...that is: cos(u+v) = cos(u)cos(v)-sin(u)sin(v)

so

cos(11pi/12)

= cos(pi/4 + 2pi/3)

= cos(pi/4)cos(2pi/3) - sin(pi/4)sin(2pi/3)

= [sqrt(2)/2][-1/2] - [sqrt(2)/2][sqrt(3)/2]

= -sqrt(2)/4 - sqrt(6)/4

= -[sqrt(6)+sqrt(2)]/4

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