# Product To Sum for trigonometry

• May 22nd 2008, 06:30 PM
>_<SHY_GUY>_<
Product To Sum for trigonometry
write:

6sin[theta] * sin6[theta]
as a sum or difference.

write cos5[theta]+ cos3[theta] as a product
• May 22nd 2008, 06:47 PM
Jhevon
Quote:

Originally Posted by >_<SHY_GUY>_<
write:

6sin[theta] * sin6[theta]
as a sum or difference.

write cos5[theta]+ cos3[theta] as a product

do you know the product to sum and the sum to product formulas?

$\sin A \sin B = \frac 12 [ \cos (A - B) - \cos (A + B)]$

$\cos A + \cos B = 2 \cos \frac {A + B}2 \cos \frac {A - B}2$

Hope that helps
• May 22nd 2008, 06:47 PM
galactus
Quote:

write cos5[theta]+ cos3[theta] as a product
Use $cos(u)+cos(v)=2cos\left(\frac{u+v}{2}\right)cos\le ft(\frac{u-v}{2}\right)$

$2cos\left(4{\theta}\right)cos({\theta})$
• May 22nd 2008, 06:53 PM
>_<SHY_GUY>_<
Quote:

Originally Posted by Jhevon
do you know the product to sum and the sum to product formulas?

$\sin A \sin B = \frac 12 [ \cos (A - B) - \cos (A + B)]$

$\cos A + \cos B = 2 \cos \frac {A + B}2 \cos \frac {A - B}2$

Hope that helps

i used it, and got 3(-2cos[theta] - cos10[theta]) but the answer is 2 instead of -2... how?
• May 22nd 2008, 06:56 PM
>_<SHY_GUY>_<
Quote:

Originally Posted by galactus
Use $cos(u)+cos(v)=2cos\left(\frac{u+v}{2}\right)cos\le ft(\frac{u-v}{2}\right)$

$2cos\left(4{\theta}\right)cos({\theta})$

when would you know when to use the double-angle formula and half angle formula? and how can you use the power reducing formula...they confuse me a lot(Angry)
• May 22nd 2008, 07:02 PM
Mathstud28
Quote:

Originally Posted by >_<SHY_GUY>_<
when would you know when to use the double-angle formula and half angle formula? and how can you use the power reducing formula...they confuse me a lot(Angry)

$\cos^{2m}(x)$ or

$\sin^{2m}(x)$

where $m\in\mathbb{N}$

$\sin^{2m+1}(x)$

or $\cos^{2m+1}(x)$

$m\in\mathbb{Z^{+}}$

use pythagorean identity

$\sin\bigg(\frac{x}{2}\bigg)$

or $\cos\bigg(\frac{x}{2}\bigg)$

use half-angle formulas

$\cos(2mx)$

or $\sin(2mx)$

and $m\in\mathbb{N}$

use double angle formuals

NOTE the restrictions on m arent neccasary, but if m does not satisfy those conditions it is tricker because you get into radicals and such
• May 22nd 2008, 07:31 PM
>_<SHY_GUY>_<
Quote:

Originally Posted by Mathstud28
$\cos^{2m}(x)$ or

$\sin^{2m}(x)$

where $m\in\mathbb{N}$

$\sin^{2m+1}(x)$

or $\cos^{2m+1}(x)$

$m\in\mathbb{Z^{+}}$

use pythagorean identity

$\sin\bigg(\frac{x}{2}\bigg)$

or $\cos\bigg(\frac{x}{2}\bigg)$

use half-angle formulas

$\cos(2mx)$

or $\sin(2mx)$

and $m\in\mathbb{N}$

use double angle formuals

NOTE the restrictions on m arent neccasary, but if m does not satisfy those conditions it is tricker because you get into radicals and such

Sorry... i didnt get one thing what you said...i just wanted to know when you use and not use those formulas(Nod)
• May 22nd 2008, 08:07 PM
Mathstud28
Quote:

Originally Posted by >_<SHY_GUY>_<
Sorry... i didnt get one thing what you said...i just wanted to know when you use and not use those formulas(Nod)

Thats what I told you...if you look closely the m just represents a natural number 1,2,3,4...

So when you have a trig function in that form use which one I said