Given that sin pie/6 = 1/3,

Question

use an equivalent trigonometric expression to show that
cos pie/3 = 1/2.

Answer 1

First of all
sin pi/6 = 1/2 not 1/3,

recall that cos 2A = 1 - 2sin^2 A
then
sin pi/3 = 1 - 2(1/2)^2
= 1 - 2(1/4)
= 1 - 1/2
= 1/2

Or we could use the fact that
cos (theta) = sin (pi/2 - theta)
cos pi/3 = sin (pi/2 - pi/3)
= sin pi/6
= 1/2

or
since we can get both sines and cosine values by knowing that ratios of sides of the 30-60-90 triangle, we could have just stated that cos pi/3 or cos 60º = 1/2, just like they found
sin pi/6 = 1/2