How do you Find on a unit circle that corresponds to t = 5 π /6.
and im also having trouble Finding the exact value of i dnt no how to get the exact value
The function you want is
$\displaystyle \omega:[0,2\pi] \to \{(x,y)|x\in [-1,1]) \mbox{ and } y \in [-1,1] $
$\displaystyle \omega(t)=(\cos(t),sin(t))$
$\displaystyle \omega\left( \frac{5\pi}{6}\right)=(\cos\left( \frac{5\pi}{6}\right),\\sin\left( \frac{5\pi}{6}\right))=\left( \frac{-\sqrt{3}}{2},\frac{1}{2}\right)$
Remember that we can rewrite coterminal angles by adding (or subtracting ) multiples of 2 Pi.
$\displaystyle \frac{31\pi}{3}=10\pi+\frac{\pi}{3}$
The first tells us to go around the unit circle 5 times (10 Pi radians)and the Pi/3 more times so
$\displaystyle \frac{31\pi}{3}\mbox{ and }\frac{\pi}{3}$
Will have the same out put for trig functions.
$\displaystyle \cos\left( \frac{31\pi}{3}\right)= \cos\left( \frac{\pi}{3}\right)=\frac{1}{2} $
This diagram should help you discover that sine is an odd function.
Take a look and see if you can convince yourself. If you have any more questions just ask.