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

thank you very much!:)

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? :)

Yes thank you very much!