Question

Find the exact value of cos(19pi/12)

Answer 1

well, notice that 19/12 is really
10/12 + 9/12 which simplified will be 5/6 + 3/4

so use that :)

Answer 2

and you'd surely have those in your Unit Circle

Answer 3

that would make it 285 degrees

Answer 4

well, it'll be a value, the cosine, no the arcCosine, the angle itself

Answer 5

\(\bf cos\left(\cfrac{19\pi}{12}\right) \implies
cos\left(\cfrac{10\pi}{12}+\cfrac{9\pi}{12}\right)
\implies cos\left(\cfrac{5\pi}{6}+\cfrac{3\pi}{4}\right)\\
cos(a+b) = cos(a)cos(b) - sin(a)sin(b)\)

Answer 6

cos(5pi/6) cos(3pi/4) - sin(5pi/6) sin(3pi/4)

Answer 7

How do I go from there?

Answer 8

those are common values, I assume you have a Unit Circle?

Answer 9

yes

Answer 10

then just get the values off the Unit Circle :)

Answer 11

do you mean the degrees?

Answer 12

the cosine and sine values for the angle, maybe you need a better unit circle, with radians and cosine and sine values => http://i.stack.imgur.com/r8uHr.gif

Answer 13

as you can see in the upper-right-hand corner, the value pair is the (cos, sin)

Answer 14

I'm still confused

Answer 15

ok.... what confuses you?

Answer 16

How do you get the value of cos(5pi/6) from the unit circle?

Answer 17

actually I get it

Answer 18

[-squareroot of (3)/2 times -squareroot of (2)/2] - [1/2 times squareroot of (2)/2]

Answer 19

5pi/6 is really just 150 degrees
in the unit circle next to that, you'll see a pair like => \( \bf \left(-\cfrac{\sqrt{3}}{2},\cfrac{1}{2}\right)\)

Answer 20

right

Answer 21

square root of (6)/4 - square root of (2)/4

Answer 22

\(\left(-\cfrac{\sqrt{3}}{2},\cfrac{1}{2}\right) \implies (cos,sin)\)

Answer 23

\[[\sqrt{6}-\sqrt{2}]/4\]

Answer 24

yes

Answer 25

thanks for helping

Answer 26

yw