Question

Find an exact value: cos(pi/12)

Answer 1

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 2

im sorry but thats not one of my options

Answer 3

i somehow have to use the sum and difference formulas

Answer 4

Are they in numerical values?

Answer 5

yes they all have sqrt6 and sqrt2 over 4 but with different signs +/-

Answer 6

cos^2(x)-sin^2(x)=cos(2x)
is from the double angle formula.

Answer 7

how would you split pi/12? i think thats what i need to do?

Answer 8

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
Why don't you post the options if you're not sure?

Answer 9

ok i think i got it thanks!!

Answer 10

yw! :)