Question

use product-to-sum to write as a sum or difference 12sin(pi/8)cos(pi/8)

Answer 1

\[\sin(2\alpha)=2\sin(\alpha)\cos(\alpha)\] here \(\alpha =\frac{\pi}{8}\) so
\(2\alpha =\frac{\pi}{4}\)

Answer 2

so you have
\[6\times 2\sin(\frac{\pi}{8})\cos(\frac{\pi}{8})\]
\[=6\times \sin(\frac{\pi}{4})=6\times \frac{\sqrt{2}}{2}=3\sqrt{2}\]

Answer 3

Okay, and you're 100% sure of this ?
you how did you get the radical 2/2 ? from the unit circle ?

Answer 4

because i recall what
\(\sin(\frac{\pi}{4})\) is as it is a fairly common one. but you can check the unit circle on the last page of the cheat sheet i am attaching and you will see that \(\sin(\frac{\pi}{4})=\frac{\sqrt{2}}{2}\)

Answer 5

you seem skeptical (which is a good thing)
did i make a mistake?

Answer 6

nope, it seems good(: I just wanna make sure I understand it correctly. Nothing worst than learning something wrong(:

Answer 7

Thank you. I'm posting 2 more like this and a verifying identity if you wanna take a look in a minute(:

Answer 8

you know what they say, "trust, yet verify"
http://www.wolframalpha.com/input/?i=12sin%28pi%2F8%29cos%28pi%2F8%29

Answer 9

haha true, thank you :D