Question

Find exact value of
cos (-5pi/12)

Answer 1

You could use the identity cos (A + B)

Answer 2

This would be cos(-45 + (-30)).

Answer 3

That expands to\[\cos(-45)\cos(-30)-\sin(-45)\sin(-30)\]

Answer 4

Each of those has values you can sub in.

Answer 5

\[\cos(-45)=\frac{ \sqrt{2} }{ 2 }\]\[\sin(-45)=-\frac{ \sqrt{2} }{ 2 }\]\[\cos(-30)=\frac{ \sqrt{3} }{ 2 }\]\[\sin(-30)=-\frac{ 1 }{ 2 }\]

Answer 6

So fill in your values now:

Answer 7

\[(\frac{ \sqrt{2} }{ 2})(\frac{ \sqrt{3} }{ 2 })-(-\frac{ \sqrt{2} }{ 2 })(-\frac{ 1 }{ 2 })\]

Answer 8

Thank you so much. I got
\[\frac{ \sqrt{6 - \sqrt{2}} }{ 4 }\]

Answer 9

That comes out to be\[\frac{ \sqrt{6}-\sqrt{2} }{ 4 }\]

Answer 10

Thank you :)

Answer 11

You're welcome!

Answer 12

Crazy answer, but that is it!