trigo problem no. 23

**afeasfaerw23231233** · March 20th 2008, 05:14 AM

trigo problem no. 23
p213 q14
Thanks

**TKHunny** · March 20th 2008, 07:55 AM

I think the important word you are missing is "suitable". You should have THREE double-angle formulas for cosine.

$\cos(2\theta)\;=\;2\cos^{2}(\theta)-1\;=\;1-2\sin^{2}(\theta)\;=\;\cos^{2}(\theta)-\sin^{2}(\theta)$

I believe you will find the last most "suitable" for your conditions. It factors as a difference of squares and should be obvious from there.

**afeasfaerw23231233** · March 21st 2008, 05:47 AM

that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!

**topsquark** · March 21st 2008, 08:14 AM

Originally Posted by afeasfaerw23231233

that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!

It is a quite useful hint. In fact, I think it's rather clever.
$cos(2\theta) = sin(\theta) + cos(\theta)$

Now use the hint: $cos(2\theta) = cos^2(\theta) - sin^2(\theta)$

$cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)$

Now factor the left hand side and see what comes of it.

-Dan

**afeasfaerw23231233** · March 21st 2008, 10:45 AM

Originally Posted by topsquark

It is a quite useful hint. In fact, I think it's rather clever.
$cos(2\theta) = sin(\theta) + cos(\theta)$

Now use the hint: $cos(2\theta) = cos^2(\theta) - sin^2(\theta)$

$cos^2(\theta) - sin^2(\theta) = cos(\theta) + sin(\theta)$

Now factor the left hand side and see what comes of it.

-Dan

thank you for your help! why i thought of it for such a long time but couldn't see it. thanks again.
EDIT: ah.. TKhunny already gave the hint to me but i was in a hurry and didn't see it. how stupid i am....

**topsquark** · March 21st 2008, 01:28 PM

Originally Posted by afeasfaerw23231233

thank you for your help! why i thought of it for such a long time but couldn't see it. thanks again.
EDIT: ah.. TKhunny already gave the hint to me but i was in a hurry and didn't see it. how stupid i am....

Not stupid...you've just not had enough experience at it. This is how you get experience.

-Dan

**TKHunny** · March 22nd 2008, 06:59 AM

Let's put a couple of things on your list of things to learn:

1) Have a little patience with yourself. No sense beating yourself up. Not everything is easy.

2) Just a little LaTeX can go a long way. It takes up WAY less space than scanned images.

Good deal. What else are you working on?

Thread: trigo problem no. 23

LinkBack

Thread Tools

Display

trigo problem no. 23

Similar Math Help Forum Discussions

trigo problem

trigo problem no. 21

trigo problem no. 14

trigo problem no. 11

trigo problem no. 9

Search Tags