Question

find an exact value of cos 165 degrees help :)?

Answer 1

i think i might get it but not to sure

Answer 2

I got it!
\[\cos(165) = \cos(120 + 45) = \cos(120)\cos(45) - \sin(120)\sin(45) \]
\[= \frac{-1}{2} \frac{1}{\sqrt2}-\frac{\sqrt3}{2}\frac{1}{\sqrt2}\]
Simply use:
\[\cos(A \pm B) = \cos(A)\cos(B) \mp \sin(A)\sin(B)\]

Answer 3

\[-\sqrt{6}-\sqrt{2} \] over 4?

Answer 4

you could also use the 1/2 angle formula
cos(165) = -cos(15) = - cos(30/2)

Answer 5

i just don't get how to plug in to all this stuff you guys are giving me

Answer 6

but your value looks good.
you can use a calculator and compare "decimal values" as a check

Answer 7

when my answer is on a form like i showed above the decimal i get is like.99 something how can that check it?

Answer 8

notice you solved cos(15) in your previous problem.

you should be -0.96592586

make sure you are in degree mode (and not radian mode)

Answer 9

and i get .9659 for cos 15 but my answers look like this that i can pick from
quantity square root of six plus square root of two divided by four.

quantity negative square root of two plus square root of six divided by four.

quantity negative square root of six minus square root of two divided by four.

quantity negative square root of six plus one divided by four.

Answer 10

your answer up above is correct
-(sqr(6)+sqr(2))/4

if you use your calculator, this expression will match -0.96592586

Answer 11

in short, do not use the calculator, add up the fractions only, leave it as rational

Answer 12

ok sweet thanks guys ok now heres were im confused i k now how to fin an exact value for
cosine of nineteen pi divided by twelve.

Answer 13

It looks like they want you to use sums and differences formulas

cos(A+B)= cos(A)cos(B)- sin(A)sin(B)
and
cos(A-B) = cos(A) cos(B)+ sin(A)sin(B)

Answer 14

I would change 19 pi/12 radians into degrees (I think better with degrees)

Answer 15

how do i know what to plug into the formula that you gave me?

Answer 16

First, find 19 pi/12 is 285 degees

if you plot this, you see it is 15 degrees past 270