Finding Angles(Factor Formulae)

**Punch** · January 19th 2010, 11:47 PM

Find all angles between 0 and $\pi$ for which $4cos\frac{A}{2}cosAsin\frac{5A}{2}=0$

**Grandad** · January 20th 2010, 12:13 AM

Hello Punch

Originally Posted by Punch

Find all angles between 0 and $\pi$ for which $4cos\frac{A}{2}cosAsin\frac{5A}{2}=0$

Given that

$4\cos\frac{A}{2}\cos A\sin\frac{5A}{2}=0$

any of these three factors could be zero. So you must solve:

$\cos\frac{A}{2}=0$

and

$\cos A=0$

and

$\sin\frac{5A}{2}=0$

Can you do that?

Grandad

**Punch** · January 20th 2010, 12:30 AM

Originally Posted by Grandad

Hello PunchGiven that

$4\cos\frac{A}{2}\cos A\sin\frac{5A}{2}=0$

any of these three factors could be zero. So you must solve:

$\cos\frac{A}{2}=0$

and

$\cos A=0$

and

$\sin\frac{5A}{2}=0$

Can you do that?

Grandad

Never Thought it to be like this, thanks

**Punch** · January 20th 2010, 01:22 AM

Just a little question if $<br /> \sin\frac{5A}{2}=0<br />$ , then in what quadrants does A lies in? Does zero means that it is positive or negative?

Edit: Found out that zero is neutral and it belongs to all quadrant.

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