# Cosine/Sine

• Jan 5th 2009, 04:32 PM
ChrisBosh
Cosine/Sine
Hey guys Im new here and I am hoping I can get some help.

write the following as a product of sine and/or cosine of the angles sin (B+C-a) + sin (C+A-B) + sin (A+B-c)-sin (A+B+C)
• Jan 5th 2009, 04:45 PM
Jhevon
Quote:

Originally Posted by ChrisBosh
Hey guys Im new here and I am hoping I can get some help.

write the following as a product of sine and/or cosine of the angles sin (B+C-a) + sin (C+A-B) + sin (A+B-c)-sin (A+B+C)

just apply the addition formula for sine (and cosine) over and over

Recall: $\displaystyle \sin (\alpha + \beta ) = \sin \alpha \cos \beta + \sin \beta \cos \alpha$

and $\displaystyle \cos (\alpha + \beta ) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$

Now, you have three terms in the sum for the angles. just apply the rules two at a time

example: $\displaystyle \sin (A + B + C) = \sin [(A + B) + C] = \sin (A + B) \cos C + \sin C \cos (A + B)$

and then you can apply the formulas i mentioned on $\displaystyle \sin (A + B)$ and $\displaystyle \cos (A + B)$
• Jan 5th 2009, 05:10 PM
ChrisBosh
Quote:

Originally Posted by Jhevon
just apply the addition formula for sine (and cosine) over and over

Recall: $\displaystyle \sin (\alpha + \beta ) = \sin \alpha \cos \beta + \sin \beta \cos \alpha$

and $\displaystyle \cos (\alpha + \beta ) = \cos \alpha \cos \beta - \sin \alpha \sin \beta$

Now, you have three terms in the sum for the angles. just apply the rules two at a time

example: $\displaystyle \sin (A + B + C) = \sin [(A + B) + C] = \sin (A + B) \cos C + \sin C \cos (A + B)$

and then you can apply the formulas i mentioned on $\displaystyle \sin (A + B)$ and $\displaystyle \cos (A + B)$

thank you so much man. really appreciate it. i remember this now.