# [SOLVED] Given sin (pi/6)=1/2 use an equivalent trig expression to show cos 2pi/3=-1/

• Apr 6th 2009, 11:27 AM
jepal
[SOLVED] Given sin (pi/6)=1/2 use an equivalent trig expression to show cos 2pi/3=-1/
which cofunction identities would u use
cos (x+pi/2)=-sinx or sin (x+pi/2)=cosx? how did u determine which one to use?
• Apr 6th 2009, 11:58 AM
stapel
Quote:

Originally Posted by jepal
which cofunction identities would u use
cos (x+pi/2)=-sinx or sin (x+pi/2)=cosx? how did u determine which one to use?

What you use will probably vary with your personal preference and the context. Did you have some particular exercise in mind?
• Apr 6th 2009, 12:00 PM
jepal
Quote:

Originally Posted by stapel
What you use will probably vary with your personal preference and the context. Did you have some particular exercise in mind?

here:

sin (pi/6)=1/2 use an equivalent trig expression to show cos 2pi/3=-1/2
• Apr 6th 2009, 12:29 PM
icemanfan
Quote:

Originally Posted by jepal
here:

sin (pi/6)=1/2 use an equivalent trig expression to show cos 2pi/3=-1/2

$\displaystyle \sin (\frac{\pi}{6}) = \frac{1}{2}$

$\displaystyle \sin (\theta) = \cos (\frac{\pi}{2} - \theta)$

Hence, $\displaystyle \cos (\frac{\pi}{3}) = \frac{1}{2}$

Also, $\displaystyle \cos (\pi - \theta) = -\cos (\theta)$

Therefore, $\displaystyle \cos(\frac{2\pi}{3}) = \cos (\pi - \frac{\pi}{3}) = -\cos (\frac{\pi}{3}) = -\frac{1}{2}$
• Apr 6th 2009, 12:29 PM
jepal
solved
ignore this question....i got the answer. :D