# trigonometic

• Jun 9th 2008, 04:09 AM
missjky
Exact value of trig functions
How do you Find http://ce.byu.edu/courses/hs/9990640.../TRIG41-92.bmp on a unit circle that corresponds to t = 5 π /6.

and im also having trouble Finding the exact value of http://ce.byu.edu/courses/hs/9990640.../TRIG41-89.bmpi dnt no how to get the exact value
• Jun 9th 2008, 04:56 AM
TKHunny
Think "Reference Angle". Look it up and show us what you get.
• Jun 9th 2008, 08:05 AM
TheEmptySet
Quote:

Originally Posted by missjky
Find http://ce.byu.edu/courses/hs/9990640.../TRIG41-92.bmp on a unit circle that corresponds to t = 5 π /6.
i dnt understand how you find the anwsr

The function you want is

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

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

$\omega\left( \frac{5\pi}{6}\right)=(\cos\left( \frac{5\pi}{6}\right),\\sin\left( \frac{5\pi}{6}\right))=\left( \frac{-\sqrt{3}}{2},\frac{1}{2}\right)$
• Jun 9th 2008, 08:19 AM
missjky
Quote:

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 http://ce.byu.edu/courses/hs/9990640.../TRIG41-97.png i no how to get it in decimal form but not in fraction form also

Evaluate http://ce.byu.edu/courses/hs/9990640...TRIG41-100.png

also whether f(x) = -sin x is even, odd, or neither but i think its neither is that correct
• Jun 9th 2008, 10:04 AM
TheEmptySet
Quote:

Originally Posted by missjky
thank you i understand now, so how do you Evaluate http://ce.byu.edu/courses/hs/9990640.../TRIG41-97.png i no how to get it in decimal form but not in fraction form also

Evaluate http://ce.byu.edu/courses/hs/9990640...TRIG41-100.png

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.

Attachment 6717