Question

Use the cosine sum and difference identities to find the exact value.

COS(5pi/12)

Answer 1

wow u actually use this site to study, boy was I fooled XD

Answer 2

haha wow brandi. yes i wanna learn

Answer 3

ok i found the answer........

Answer 4

"1/cos(5pi/12)

In order to find the exact value of cos(5pi/12), you must express 5pi/12 as the sum or difference of two known unit circle values. Since 5pi/12 is not among our known values of the unit circle, we cannot solve this directly.

This involves some experimentation.
Can we split 5pi/12 as 4pi/12 + pi/12? 4pi/12 reduces to pi/3, and pi/3 is a known unit circle value. However, pi/12 is NOT a known unit circle value, so we try again.
5pi/12 = 3pi/12 + 2pi/12?
This reduces to pi/4 + pi/6. Both are known unit circle values!!

Now, we use the cosine addition property:
cos(a+ b) = cos(a)cos(b) - sin(a)sin(b)

Therefore,

1/cos(5pi/12) =
1/cos(3pi/12 + 2pi/12) =
1/cos(pi/4 + pi/6) =
1/[ cos(pi/4)cos(pi/6) - sin(pi/4)sin(pi/6) ] =
1/[ (sqrt(2)/2) (sqrt(3)/2) - (sqrt(2)/2) (1/2) ] =
1/[ sqrt(6)/4 - sqrt(2)/4 ] =
1/ ( [ sqrt(6) - sqrt(2)]/4 )

So we then just take the reciprocal.

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

Of course, the simplified answer would probably have the denominator rationalized.
Multiply top and bottom by the bottom's conjugate.

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

Which reduces to just

sqrt(6) + sqrt(2)"

Answer 5

google?

Answer 6

no, yahoo....... XD