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Now, this isn't as much of a question about how to find the exact value, as it is a quesiton of algebra.
I am to find the exact value of cos 105º. I'll do that by using the exact values of 60 and 45. Thus exact value of cos 60º + exact value of 45º, being the root of 2 over 2 and 1 over 2, respectivily. My question is a simple as this:
Well you can write that as :
Or:
(because
)You can write it as any of the above... I don't think there is a way to make it any simpler than those.
Last edited by polylog (2006-11-01 12:54:30)
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There's a mistake in the second line of working there because you've started with 1/√2 instead of 1/2.
However, the question is wrong anyway, because cos 105 ≠ cos 60 + cos 45.
You need to use the addition formula, namely cos(A+B) = cosAcosB - sinAsinB.
Using 60 and 45, this gets us cos60cos45 - sin60sin45.
Why did the vector cross the road?
It wanted to be normal.
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Oops, fixed.
Thanks.
Two lessons for me: thinking more about Latex and less about algebra is bad - and: never assume the work so far is correct !
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