adding and subtracting

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December 6th 2008, 08:24 AM
Crazyheaven

adding and subtracting

1. cos 3pie/7(cos 2pie/21)+ sin 3pie/7(sin 2pie/21)

2. (tan 73 degrees - tan 13 degrees)/ (1+ tan 73 degrees tan 13 degrees)

Write the expression as a trigonometric function of one number, and then find its exact value.

I'm new to trig and it really confuses me. My book doesn't really give me examples of some of the problems it ask me to solve. Would someone here be willing to work these problem or ones like them to show me step by step how to solve it?

I'm going to be posting quite a few questions within the next couple of days :(.
December 6th 2008, 08:39 AM
running-gag

Quote:

Originally Posted by Crazyheaven

1. cos 3pie/7(cos 2pie/21)+ sin 3pie/7(sin 2pie/21)

Do you mean

$cos(\frac{3 \pi}{7}) cos (\frac{2 \pi}{21}) + sin(\frac{3 \pi}{7}) sin (\frac{2 \pi}{21})$ ?

If so use the formula cos(a-b) = cos(a) cos(b) + sin(a) sin(b)

$cos(\frac{3 \pi}{7}) cos (\frac{2 \pi}{21}) + sin(\frac{3 \pi}{7}) sin (\frac{2 \pi}{21}) = cos(\frac{3 \pi}{7} - \frac{2 \pi}{21}) = cos(\frac{\pi}{3}) = \frac{1}{2}$
December 6th 2008, 08:40 AM
Sean12345

Hi Crazyheaven,

I assume it is supposed to read

$\cos \left(\frac{3\pi}{7}\right)\cdot\cos \left(\frac{2\pi}{21}\right)+\sin \left(\frac{3\pi}{7}\right)\cdot\sin \left(\frac{2\pi}{21}\right)$

A Key point to note is that $\cos(\theta\pm\phi)\equiv\cos\theta\cdot\cos\phi\m p\sin\theta\cdot\sin\phi$

and so the above equation can be written as

$<br /> \cos \left(\frac{3\pi}{7}-\frac{2\pi}{21}\right) = \cos \left(\frac{7\pi}{21}\right) = \cos \left(\frac{\pi}{3}\right)=\frac{1}{2}<br />$

The second is simlar and uses the identity

$\tan (\theta\pm\phi)\equiv \frac{\tan\theta\pm\tan\phi}{1\mp\tan\theta\cdot\t an\phi}$

Hope this helps.
December 6th 2008, 09:13 AM
Crazyheaven

Wow that helps out a lot. Why couldn't my book break it down like that. How do you make the little pie and times symbol so I can make my problems more clear for now on?
December 6th 2008, 11:07 AM
running-gag

Just quote our posts and you will see how to do !