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

1. ## [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?

2. 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?

3. 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

4. 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, $\displaystyle \cos(\frac{2\pi}{3}) = \cos (\pi - \frac{\pi}{3}) = -\cos (\frac{\pi}{3}) = -\frac{1}{2}$

5. ## solved

ignore this question....i got the answer.