# Re: cosines

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Posted by T.Gracken on November 13, 2002 at 20:11:48:

In Reply to: cosines posted by tracey on November 13, 2002 at 14:58:16:

: I have a question on cosines from your algebra 2 tutorial. In example 1. Find cosine of 15 degrees. It says to write 15 degrees in terms of angles with known trig values 45 and 30 degrees. I am missing the jump from 15 degrees to 45-30. Can you explain why those numbers were picked and what the rational behind that.

: Thanks so much!!!

first, so you know, I didn't write the tutorial (or anything else here except the posts on this message board). but I'll try to explain.

since we know the values of cosine for 0o, 30o, 45o, 60o, and 90o, we can sometimes use these values to determine other unknown values using them.

However, we must also use other identities.

one of the identities we have available is

cos(u-v) = cos(u)cos(v)+sin(u)sin(v)

since 15o is equal to 45o-30o, we can rewrite

cos(15o) as cos(45o-30o)

now using the identity above (sometimes called a difference identity) we can calulate cos(15o)

that is,

cos(15o)

= cos(45o-30o)

= cos(45o)cos(30o) + sin(45o)sin(30o)

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

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

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

hope that helps.

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