Posted by Anonymous on Saturday, October 31, 2009 at 12:06pm.
Given that sin pie/6 = 1/3,
use an equivalent trigonometric expression to show that
cos pie/3 = 1/2.

math  Reiny, Saturday, October 31, 2009 at 12:36pm
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 306090 triangle, we could have just stated that cos pi/3 or cos 60ยบ = 1/2, just like they found
sin pi/6 = 1/2
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