Question

find the exact value by using a half-angle identity.
sin (22.5 degrees)

Answer 1

Express \(\cos(2\theta)\) in terms of \(\sin(\theta)\) and then substitute \(\theta=22.5^0\)

Answer 2

use mathway.com

Answer 3

sqrt (2- sqrt 2)?

Answer 4

\(\bf 22.5\cdot 2\implies 45\qquad thus\qquad \cfrac{45}{2}\iff 22.5
\\ \quad \\
sin\left(\cfrac{{\color{red}{ 45^o}}}{2}\right)=\pm \sqrt{\cfrac{1-cos({\color{red}{ 45^o}})}{2}}\)

Answer 5

not quite @chris215 - if you list the steps you took then I can help you spot where you may have made a mistake

Answer 6

using the half angle formula for sin : sin((1/2)x) = 0 +/- sprt (1-cos(x) /2)

Answer 7

then i substitted 45 for x

Answer 8

and got sin(22.5) = sqrt ((1 - sqrt(2)/2))

Answer 9

what did you use for the value of cos(45)?

Answer 10

sqrt of 2

Answer 11

that is not correct

Answer 12

\[\cos(45)=\frac{1}{\sqrt{2}}=\frac{\sqrt{2}}{2}\]

Answer 13

oh yeah thats what I got sorry but next I used the positive sqrt and simplified

Answer 14

if you use that value and simplify then you do not end up with what you put above - please list your steps so I can spot where your mistake may have been

Answer 15

you can use the draw button below if that makes it easier for you

Answer 16

ok ill try my best to write it out on here

Answer 17

e.g.: