Question

How do I find the exact value of this trigonometric function?
> cos 23π/6

Answer 1

\[\cos(\frac{ 23\pi }{ 6 })\]
\[=\cos(\frac{ 23(180) }{ 6 })\]
\[=\cos(23\times30)\]
\[=\cos(690-360)\]
\[=\cos(330)\]

Answer 2

lots of ways of doing this

23/6 = 3 5/6

so its a 4th quadrant angle which has the same value as

\[\cos(\pi/6)\]



23/6 = 24/6 - 1/6

you can also use the difference of 2 angles then expand

\[\cos(\frac{24\pi}{6} - \frac{\pi}{6})\]

Answer 3

If you plug in
\[cos^{2}(330)\] into your calculator you will get
\[\frac{ 3 }{ 4 }\]
Then you can see that the exact value would be
the square root of \[\frac{ 3 }{ 4 }\]