Question

Find an exact value. cos 15°

Answer 1

is the answer (sqrt 6 + sqrt 2)/4

Answer 2

Hmm

Answer 3

\[\Large\rm \cos15=\cos\left(\frac{30}{2}\right)=\sqrt{\frac{1+\cos30}{2}}\]\[\Large\rm=\sqrt{\frac{1+\sqrt3/2}{2}}=\sqrt{\frac{2+\sqrt3}{4}}=\frac{\sqrt{2+\sqrt3}}{2}\]

Answer 4

I'm a little confused where you got that 4 from in the bottom, Hmm

Answer 5

that answer is non of my choices though

Answer 6

What are the choices? :D
Maybe you can list them.

Answer 7

These problems can be tough for multiple choice because it's hard to simplify things down to where they want.

Answer 8

yeah im pretty confused

Answer 9

Oh ok.. so notice that I have a root within a root.
So half angle formula was definitely a bad choice.
There IS A WAY to denest roots, but it's definitely annoying.

Let's go to our angle difference formula for cosine instead.

Answer 10

\[\Large\rm \cos15=\cos(45-30)\]Ya?

Answer 11

\[\Large\rm =\cos45\cos30+\sin45\sin30\]

Answer 12

yeah that's what i did

Answer 13

\[\Large\rm =\frac{\sqrt2}{2}\cdot\frac{\sqrt3}{2}+\frac{\sqrt2}{2}\cdot\frac{1}{2}\]Oh ok good :)

Answer 14

Ahh now I see where you got the 4 from ^^ hehe

Answer 15

Ah yes your answer looks correct \c:/

Answer 16

Sorry to ramble on so long lol

Answer 17

ohh ok but thanks so much I wasn't sure if I did it right or not