Question

Use the exact values of the sin 30˚, sin 45˚, cos 30˚, and cos 45˚ to find the exact value of cos 15˚.

Answer 1

because 15 = 45 - 30, we can say

cos(15) = cos(45 - 30)

now use the identity

cos(x-y) = cos(x)*cos(y) + sin(x)*sin(y)

Answer 2

in this case

x = 45
y = 30

Answer 3

is that it

Answer 4

what is cos(45)

use the unit circle to determine this

Answer 5

i have no idea

Answer 6

do you have a unit circle?

Answer 7

no

Answer 8

check out

http://upload.wikimedia.org/wikipedia/commons/thumb/4/4c/Unit_circle_angles_color.svg/720px-Unit_circle_angles_color.svg.png

Answer 9

is it radical 2/2

Answer 10

yes, \[\Large \frac{\sqrt{2}}{2}\]

Answer 11

what is cos(30) ?

Answer 12

radical 3/2

Answer 13

sin 45= √2/2

Answer 14

good, sin(30) = ??

Answer 15

sin 30=1/2

Answer 16

good

\[\Large \cos(15) = \cos(45 - 30)\]
\[\Large \cos(15) = \cos(45)\cos(30) + \sin(45)\sin(30)\]
\[\Large \cos(15) = \frac{\sqrt{2}}{2}*\frac{\sqrt{3}}{2}+\frac{\sqrt{2}}{2}*\frac{1}{2}\]
\[\Large \cos(15) = \frac{\sqrt{2}*\sqrt{3}}{2*2}+\frac{\sqrt{2}*1}{2*2}\]
\[\Large \cos(15) = \frac{\sqrt{2*3}}{2*2}+\frac{\sqrt{2}}{2*2}\]
\[\Large \cos(15) = \frac{\sqrt{6}}{4}+\frac{\sqrt{2}}{4}\]

Answer 17

actually, I just noticed that you had 2's and not 4's

so you were close

Answer 18

understood

Answer 19

since you are multiplying fraction you have to multiply both the numerator and the denominator

Answer 20

exactly, multiply straight across

Answer 21

ok thank you very much i hope to get help from you next time