1. ## Exact value of trig functions

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

2. Think "Reference Angle". Look it up and show us what you get.

3. Originally Posted by missjky
Find on a unit circle that corresponds to t = 5 π /6.
i dnt understand how you find the anwsr
The function you want is

$\omega:[0,2\pi] \to \{(x,y)|x\in [-1,1]) \mbox{ and } y \in [-1,1]$

$\omega(t)=(\cos(t),sin(t))$

$\omega\left( \frac{5\pi}{6}\right)=(\cos\left( \frac{5\pi}{6}\right),\\sin\left( \frac{5\pi}{6}\right))=\left( \frac{-\sqrt{3}}{2},\frac{1}{2}\right)$

4. Originally Posted by TheEmptySet
The function you want is

$\omega:[0,2\pi] \to \{(x,y)|x\in [-1,1]) \mbox{ and } y \in [-1,1]$

$\omega(t)=(\cos(t),sin(t))$

$\omega\left( \frac{5\pi}{6}\right)=(\cos\left( \frac{5\pi}{6}\right),\\sin\left( \frac{5\pi}{6}\right))=\left( \frac{-\sqrt{3}}{2},\frac{1}{2}\right)$
thank you i understand now, so how do you Evaluate i no how to get it in decimal form but not in fraction form also

Evaluate

also whether f(x) = -sin x is even, odd, or neither but i think its neither is that correct

5. Originally Posted by missjky
thank you i understand now, so how do you Evaluate i no how to get it in decimal form but not in fraction form also

Evaluate

also whether f(x) = -sin x is even, odd, or neither but i think its neither is that correct
Remember that we can rewrite coterminal angles by adding (or subtracting ) multiples of 2 Pi.

$\frac{31\pi}{3}=10\pi+\frac{\pi}{3}$

The first tells us to go around the unit circle 5 times (10 Pi radians)and the Pi/3 more times so

$\frac{31\pi}{3}\mbox{ and }\frac{\pi}{3}$

Will have the same out put for trig functions.

$\cos\left( \frac{31\pi}{3}\right)= \cos\left( \frac{\pi}{3}\right)=\frac{1}{2}$

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.