Question

I need exact value by using a half angle identity of sin pi/12

Answer 1

Mind looking up and then posting here the "half angle identity for the sine?"

That'd give you plenty with which to work.

Answer 2

i think you can rewriting it bc. pi/12 = 15 so you can writing sin15 what you can calculi rweriting it in this form sin15 = sin(45-30) = ...
and there use formula sin(a-b) = ...

hope you know it

Answer 3

after you distributed these so you need using these knowladge again

sin45 = sqrt2 /2
sin30 = 1/2
cos45 = sqrt2 /2
cos30 = sqrt3 /2

hope these will help you

Answer 4

Half angle for sin is sin a/2=plus or minus sqrt1-cosa/2

Answer 5

\[\cos 2 \theta=1-2\sin ^2 \theta\]
\[\sin \theta=\pm \frac{ 1 }{ 2 }\sqrt{1-\cos 2 \theta}\]
\[when ~\theta=\frac{ \pi }{ 12 }<\frac{ \pi }{ 2 },\sin \theta ~is~positive.\]
\[\sin \theta=\sqrt{1-\cos 2\theta }\]
substitute \[\theta=\frac{ \pi }{ 12 }\]
\[\cos 2\theta=\cos \frac{ \pi }{ 6 }=?\]

Answer 6

Half angle for sin is sin a/2=plus or minus sqrt1-cosa/2
\[\sin \frac{ a }{ 2 }= \pm \frac{ \sqrt{1-\cos a} }{ 2 }\]

Answer 7

Note that \[\frac{ \pi }{ 12 }=\frac{ \frac{ \pi }{ 6 } }{ 2 }\]

Answer 8

so that "a" in the formula immediately above is pi/6. It happens that cos pi/6 is \[\frac{ \sqrt{3} }{ 2 }\]

Answer 9

Substitute this value for "cos a" in the formula immediately above. Simplify your result as much as possible.