Cosine/Sine

ChrisBosh · #1 $Old$ January 5th, 2009, 06:32 PM

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)

Jhevon · #2 $Old$ January 5th, 2009, 06:45 PM

Quote:

Originally Posted by ChrisBosh $View Post$

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

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

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

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

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

ChrisBosh · #3 $Old$ January 5th, 2009, 07:10 PM

Quote:

Originally Posted by Jhevon $View Post$

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

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

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

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

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

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

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

o yes and reps added