## myininaya 5 years ago is there a way to prove that cos(pi/3)=1/2

1. anonymous

Let V be the image point corresponding with the angle pi/3 on the unit circle and let E the intersection point of that circle with the positive X-axis. The triangle 'OVE' is equilateral. sin^2 (pi/3) = sqrt( 1 - cos^2 (pi/3)) = sqrt(3)/2 So, sin(pi/3) = sqrt(3)/2 and cos(pi/3) = 1/2.

2. anonymous

if you write the cosine in terms of Euler's formula and expands in power series of the $e^{i \theta}$ and $e^{-i \theta}$ , you will get cos( pi/3)=1/2.

3. myininaya

these are cool things to know. I will be your fan :)

4. anonymous

=D

5. anonymous

:)

6. anonymous

|dw:1336890915598:dw| $\cos (\frac{\pi}{3}) = \frac{1}{2}$ hehe :P

7. myininaya

Yes I know that one Wow this was a long time ago

8. myininaya

Great job :)

9. anonymous

lol i was supposed to look at your first question then i noticed this..thanks :D

10. myininaya

i can't remember that i asked this