trigo problem no. 23

p213 q14

ThanksAttachment 5449

Attachment 5450

Attachment 5451

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- Mar 20th 2008, 05:14 AMafeasfaerw23231233trigo problem no. 23
trigo problem no. 23

p213 q14

ThanksAttachment 5449

Attachment 5450

Attachment 5451 - Mar 20th 2008, 07:55 AMTKHunny
I think the important word you are missing is "suitable". You should have THREE double-angle formulas for cosine.

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

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. - Mar 21st 2008, 05:47 AMafeasfaerw23231233
that mean the 'hint ' from the book is useless! it directs me to the wrong way to do this question!

- Mar 21st 2008, 08:14 AMtopsquark
It is a quite useful hint. In fact, I think it's rather clever.

$\displaystyle cos(2\theta) = sin(\theta) + cos(\theta)$

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

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

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

-Dan - Mar 21st 2008, 10:45 AMafeasfaerw23231233
- Mar 21st 2008, 01:28 PMtopsquark
- Mar 22nd 2008, 06:59 AMTKHunny
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?