Question

I have a question that says to "use the half-angle identities to evaluate cos(pi/8) exactly" and i can't solve it past +-√[(1+cos(pi/8))/2] ... anyone?

Answer 1

i went cos(pi/8) to cos(pi/4/2) btw

Answer 2

I got you :P
\[\cos^2(\frac{\pi}{8})=\frac{1}{2}(1+\cos(\frac{\pi}{4}))\]
Cosine is positive since pi/4 is going to give a positive x. So:
\[\cos(\frac{\pi}{8})=\frac{\sqrt{2+\sqrt{2}}}{2}\]

Answer 3

At the end, your answer will look different but I did a little manipulation to make it look nice.

Answer 4

I'm sorry.... :( I don't follow what you did......

Answer 5

Use the formula:
\[\cos^2(a)=\frac{1}{2}(1+\cos(2a))\]
a=pi/8
Can you follow from there?

Answer 6

No - I don't have that formula. I have cos(x/2)=√[(1+cosx)/2]

Answer 7

oh hell its the same thing

Answer 8

Its the same formula.
Square your formula
cos^2(x/2)=(1+cos(x))/2

Either way. Using your (same) formula you have:
\[\cos(\frac{\frac{\pi}{4}}{2})=\sqrt{\frac{1+\cos(\frac{\pi}{4})}{2}}\]

Answer 9

Then you have:
cos(pi/4)=sqrt(2)/2
\[\sqrt{\frac{1+\frac{\sqrt{2}}{2}}{2}}=\sqrt{\frac{\frac{2+\sqrt{2}}{2}}{2}}=\frac{\sqrt{2+\sqrt{2}}}{\sqrt{2}*\sqrt{2}}=\frac{\sqrt{2+\sqrt{2}}}{2}\]

Answer 10

I can't give two medals can I.

Answer 11

Haha, no :P But thank you.

Answer 12

dude you're blowin' my mind right now

Answer 13

Sorry D: Whats wrong?

Answer 14

no it's good - i can't even see what you saw until you did it. but the 1 = 2/2, so 1 + r2/2 = 2+r2 all over 2 but

Answer 15

divide two divide two equals divide 4, and r2 *r2 doesn't equal four in the denom....or?

Answer 16

jesus, wait....lol

Answer 17

smh

Answer 18

Haha, I can work it out in slightly more gruesome detail, but not much more :/

Answer 19

yeah, sorry i got it.

Answer 20

Sure?

Answer 21

100% - i don't know why i didn't apply the radical to the denominator. crap :( much thanks bud

Answer 22

No problem :P

Answer 23

chess was easily to master than trig

Answer 24

easier? yeah

Answer 25

Haha, I just made that mistake :P Any other questions just post them man :P

Answer 26

thanks bud. again much thanks.