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 using the cosine sum and difference to find values

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T O P I C    R E V I E W
Cortez Mos Posted - 10/17/2007 : 23:16:16
cos(-10)cos 35+ sin(-10) sin 35
4   L A T E S T    R E P L I E S    (Newest First)
sahsjing Posted - 10/18/2007 : 17:37:35
Another approach:
cos(-10)cos 35+ sin(-10) sin 35
= sin80 cos35 - cos 80 sin35
= sin(80-35)
= sin 45
= 2 / 2
the_hill1962 Posted - 10/18/2007 : 07:34:54
I believe the formula that royhaas is referring to is:
cos(A−B) = cos A cos B + sin A sin B
At least that is the obvious one to me from the following that you should have seen before being assigned this problem:
1. cos(A+B) = cos A cos B − sin A sin B
2. sin(A+B) = sin A cos B + cos A sin B
3. cos(A−B) = cos A cos B + sin A sin B
4. sin(A−B) = sin A cos B − cos A sin B
The reason that we pick out the 3rd one is because your problem is
cos(-10)cos 35+ sin(-10) sin 35
Notice if you have A=-10 and B=35
then your problem is
cos(A)cos(B) + sin(A)sin(B) which is EXACTLY what the 3rd identity states that cos(A-B) is equal to.
Now all you have to do is the simple problem of subtracting B from A (which in your case is -35 minus 10.
So, since you problem is equivalent to cos(A-B) where A=-10 and B=35,
it is cos(-10 - 35), and that is cos(-45).
Now, you should already know that cos(-45) is equal to (2)/2
Cortez Mos Posted - 10/17/2007 : 23:25:35
example please
royhaas Posted - 10/17/2007 : 23:24:30
Just plug into the formula and simplify.

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