Question

Find an exact value.

cos 15°

Answer 1

cos(45-30)
using cos(A-B)=cosAcosB+sinAsinB

Answer 2

Got?

Answer 3

cos (45 - 30) = cos45cos30 + sin45sin30 ?

Answer 4

yes

Answer 5

Can you solve now?

Answer 6

so then would it be cos (45-30) = (radical) 2 / 2 * (radical) 3 / 2 + (radical) 2 / 2 * 1 / 2 ?

Answer 7

would it be \[\sqrt{6} + \sqrt{2} / 4\]

Answer 8

It should be Sqrt[3] - 1/2 Sqrt[2]

Answer 9

1/sqrt(2)*sqrt(3)/2 - 1/sqrt(2)*1/2

Answer 10

=sqrt(3)-1 / 2sqrt(2)

Answer 11

Got it?

Answer 12

thats not one of my answer choices :(

Answer 13

these are my answer choices

Answer 14

okay let me see....

Answer 15

@lxoser
cos(15)

To find this value, all you have to do is express 15 as a sum or difference of two known unit circle values. Then, take advantage of the sum/difference identities.

cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
cos(a - b) = cos(a)cos(b) + sin(a)sin(b)

[note: watch how the addition one uses subtraction, and subtraction uses addition]

For this case, 15 = 45 - 30. Therefore,

cos(15) =
cos(45 - 30)

And we know what the sine and cosine of 45 degrees and 30 degrees are. Using the cosine difference identity, we get

cos(45)cos(30) + sin(45)sin(30)

Which we know how to solve.

(sqrt(2)/2) (sqrt(3)/2) + (sqrt(2)/2) (1/2)

Keep simplifying,

[ sqrt(6)/4 ] + [ sqrt(2) / 4 ]
[sqrt(6) + sqrt(2)] / 4

Answer 16

its A

Answer 17

so i got it right the first time, thank you so much guys for your time & help! i understand now :-)

Answer 18

i live in florida

Answer 19

is that FLVS?

Answer 20

lol, yes it is

Answer 21

i completely agree!! lol

Answer 22

i like how if you miss one you get an 80 on the homework

Answer 23

yeah i know! like really?

Answer 24

and it brings your grade down like 2-3 points but if you get a 100 it brings it up like .25

Answer 25

lmao omg i feel your pain so much

Answer 26

what math are you in

Answer 27

what math are you in

Answer 28

im in pre-cal honors

Answer 29

if you go to google and type in flvs it got a 2.5 on google but flvs only shows the good ones on the side XD

Answer 30

lol, really?? florida students got it rough lol