Question

is there a way to prove that cos(pi/3)=1/2

Answer 1

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.

Answer 2

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.

Answer 3

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

Answer 4

=D

Answer 5

:)

Answer 6

\[\cos (\frac{\pi}{3}) = \frac{1}{2}\] hehe :P