Thread: Trig Help
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  #5  
Old October 7th, 2007, 07:52 PM
Soroban Soroban is offline
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Hello again, mmgolf!

For #2, you need some Sum/Difference formulas.

Quote:
2. Find the exact value for:
(a)\;\;\tan105
(b)\;\;\sin195
(c)\;\;\cos51\cos9 - \sin51\sin9
(a)\;\;\tan105^o

We note that: .105 \:=\:60 + 45
. . and we use: .\tan(A + B)\:=\:\frac{\tan A + \tan B}{1 - \tan A\tan B}

Hence we have: .\tan105 \:=\:\tan(60 + 45) \;=\;\frac{\tan60 + \tan45}{1 - \tan60\tan45}

Can you finish it now?


Quote:
(b)\;\;\sin195^o

Note that: .195 \:=\:150 + 45
. ,and we use: .\sin(A + B) \:=\:\sin A\cos B + \sin B\cos A

So we have: .\sin(150 + 45) \:=\:\sin150\cos45 + \sin45\cos150 . . . etc.


Quote:
(c)\;\;\cos51\cos9 - \sin51\sin9
You're expected to recognize that this is the right side of the formula:
. . \cos(A + B) \:=\:\cos A\cos B - \sin A\sin B

Got it?
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