## anonymous one year ago Find an exact value. cos 15°

1. arindameducationusc

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

2. arindameducationusc

Got?

3. anonymous

cos (45 - 30) = cos45cos30 + sin45sin30 ?

4. arindameducationusc

yes

5. arindameducationusc

Can you solve now?

6. anonymous

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

7. anonymous

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

8. arindameducationusc

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

9. arindameducationusc

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

10. arindameducationusc

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

11. arindameducationusc

Got it?

12. anonymous

thats not one of my answer choices :(

13. anonymous

14. arindameducationusc

okay let me see....

15. anonymous

@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

16. anonymous

its A

17. anonymous

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

18. anonymous

i live in florida

19. anonymous

is that FLVS?

20. anonymous

lol, yes it is

21. anonymous

i completely agree!! lol

22. anonymous

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

23. anonymous

yeah i know! like really?

24. anonymous

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

25. anonymous

lmao omg i feel your pain so much

26. anonymous

what math are you in

27. anonymous

what math are you in

28. anonymous

im in pre-cal honors

29. anonymous

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

30. anonymous

lol, really?? florida students got it rough lol