Question

Express the given product as a sum or difference containing only sines or cosines.

sin(8x)cos(6x)

Answer 1

Do you know the Product to Sum formula?

Answer 2

Learning it right now

Answer 3

ah it's sin u cos v

Answer 4

Sorry this is the first problem like this I've seen

Answer 5

hm maybe you didn't sub in the u and v but this would look the same.
u=8x
v= 6x

\[\sin (u)\cos(v) = \frac{ 1 }{ 2 } (\sin(u+v) + \sin(u-v))\]
After plugging in u=8x v= 6x
\[\sin (8x)\cos(6x) = \frac{ 1 }{ 2 } (\sin(8x+6x) + \sin(8x-6x))\]

does this look familiar?

Answer 6

yes

Answer 7

\[\ = \frac{ 1 }{ 2 } (\sin(14x) + \sin(2x))\]

and that's how you do it.

The left side is just the original equation that we transfer from product to sum.

Answer 8

Got it! thank you for explaining!

Answer 9

\(\color{salmon}{\large\heartsuit}\large\text{You're Most Welcome! }\color{salmon}\heartsuit\)
\(~~~~~~~~~~~~~~~\color{green}{\large\ddot\smile}\color{blue}{\large\ddot\smile}\color{salmon}{\large\ddot\smile}\color{blue}{\large\ddot\smile}\color{salmon}{\large\ddot\smile}\)
\(~~~~~~~~~~~~~~~~~~~~\color{salmon}{\large\bigstar}\color{salmon}{\large\bigstar}\color{salmon}{\large\bigstar} \)

Answer 10

sin(9x)cos(5x)=1/2sin(14x)+sin(4x)

is that correct?

Answer 11

Yes :)

Answer 12

woohoo! haha