Question

Find an exact value.

cosine of nineteen pi divided by twelve.

Answer 1

You will need to evaluate each option to see if it evaluates to:
sqrt((1+sqrt(3)/2)/2)
which can be written as
sqrt((2+sqrt(3)/4)
or
sqrt(2+sqrt(3)/2

Answer 2

im confused how did you go from cosine to squareroots

Answer 3

let y=cos(pi/12), then
apply the double angle formula:
cos^2(x)-sin^2(x)=cos(2x)
or, substituting sin^2(x)+cos^2(x)=1,
2cos^2(x)-1=cos(2x)
cos^2(x)=(1+cos(2x))/2
let x=pi/12
then
cos^2(pi/12)=(1+cos(pi/6))/2
Since cos(pi/6) is known to be sqrt(3)/2,
cos(pi/12)=sqrt((1+sqrt(3)/2)/2)

Answer 4

but the question asks for cos(19pi/12)

Answer 5

What Are Your Options To Choose From?