Question

Find an exact value.

cosine of negative seven pi divided by twelve

Answer 1

\[\cos(-7 \pi/12)=\cos(7 \pi/12)=\cos(\frac{ 6 \pi+\pi }{ 12 })=\cos(\frac{ \pi }{ 2 }+\frac{ \pi }{ 12 })=-\sin(\frac{ \pi }{ 12 })\]and we know that:\[\sin(\alpha)=\sqrt{\frac{ 1-\cos(2 \alpha) }{ 2 }}\rightarrow -\sin(\pi/12)=-\sqrt{\frac{ 1-\cos(\pi/6) }{ 2 }}\]and \[\cos(\pi/6)=\cos(30º)=\sqrt{3}/2\]then\[\cos(-7\pi/12)=-\sqrt{\frac{ 1-\frac{ \sqrt{3} }{ 2 } }{ 2 }}=-\sqrt{\frac{ 2-\sqrt{3} }{ 4 }}=-\frac{ 1 }{ 2 }\sqrt{2-\sqrt{3}}\]

Answer 2

that just looks like a bunch of weird stuff is there any way I can turn the eqautions on?

Answer 3

if you find it weird i can withdraw it but it is the way to go. If you find something easier, let me know. This is about calculating the cosine of a weird angle using known values of pupular angle like 30º

Answer 4

no I mean like the eqautoion system isn't working I just see a bhunch of symbols one day I just couldn't see eqautions anymore

Answer 5

\[\frac{ 7 }{ 5}\] like when I do that it looks funny

Answer 6

with my calculator: cos(-7pi/12)=-0.258819045

Answer 7

yea but my answers look like this
square root of six plus square root of two

quantity square root of six minus square root of two divided by four

square root of two minus square root of six

quantity square root of two minus square root of six divided by four

Answer 8

if none of the choices is negative, none is valid