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lorraine_09 · Jul 27, 2009, 07:58 AM

Find the exact value for cos 105 degrees (No credit for a decimal answer from a calculator!)

thank you very much!:)

Unknown008 · Jul 27, 2009, 09:05 AM

You know the basic identities?

$cos 30 = \frac{\sqrt3}{2}$

$cos 60 = \frac12$

$cos 45 = \frac{1}{\sqrt2}$

$sin 30 = \frac12$

$sin 60 = \frac{\sqrt3}{2}$

$sin 45 = \frac{1}{\sqrt2}$

Well, you'll use them here.

What is 105?

It is 45 + 60.

So, $cos(105) = cos (45+60)$

but cos(A+B) = cos A cosB - sin A sin B[/math]

So, cos (105) = cos (45+60) = cos 45 cos 60 - sin 45 sin 60

Can you do it now? :)

lorraine_09 · Jul 27, 2009, 09:13 AM

Yes thank you very much!