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 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

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