Find sin(2A) if A is an acute angle with cos A = 1/3. Please help!!

**right-as-rain** · December 3rd 2008, 02:47 PM

I'm stuck. All help is greatly appreciated.

**11rdc11** · December 3rd 2008, 02:59 PM

Ok since the problem stated that cos is a acute angle that means you in the 1st quad so your sin is going to be positive as well.

Now use pyth to figure out what sin A is

$y^2 + 1^2 = 3^2$

$y^2 = 8$

$y = 2\sqrt{2}$

so

$\sin {A} = \frac{2\sqrt{2}}{3}$

Now

$\sin{2A} = 2\sin{A}\cos{A}$

Can you finish up

**right-as-rain** · December 3rd 2008, 03:03 PM

Thanks very much. I'll see what I can do.

**right-as-rain** · December 3rd 2008, 03:09 PM

Does it work out to:

4(square root 2)/9 ?

**11rdc11** · December 3rd 2008, 03:21 PM

Originally Posted by right-as-rain

Does it work out to:

4(square root 2)/9 ?

You tell me

$2\sin{A}\sin{A}$

and knowing

$\sin {A} = \frac{2\sqrt{2}}{3}$

$\cos {A} = \frac{1}{3}$

so just plug in

$\bigg(2\bigg)\bigg(\frac{2\sqrt{2}}{3}\bigg)\bigg( \frac{1}{3}\bigg) = \frac{4\sqrt{2}}{9}$

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