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 Geometry and Trigonometry
 using the cosine sum and difference to find values
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Cortez Mos
Junior Member

USA
3 Posts

Posted - 10/17/2007 :  23:16:16  Show Profile  Reply with Quote
cos(-10)cos 35+ sin(-10) sin 35
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royhaas
Moderator

USA
3059 Posts

Posted - 10/17/2007 :  23:24:30  Show Profile  Reply with Quote
Just plug into the formula and simplify.
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Cortez Mos
Junior Member

USA
3 Posts

Posted - 10/17/2007 :  23:25:35  Show Profile  Reply with Quote
example please
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the_hill1962
Advanced Member

USA
1468 Posts

Posted - 10/18/2007 :  07:34:54  Show Profile  Reply with Quote
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.
-35-10=-45
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
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sahsjing
Advanced Member

USA
2399 Posts

Posted - 10/18/2007 :  17:37:35  Show Profile  Reply with Quote
Another approach:
cos(-10)cos 35+ sin(-10) sin 35
= sin80 cos35 - cos 80 sin35
= sin(80-35)
= sin 45
= 2 / 2
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