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math

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Given that sin pie/6 = 1/3,
use an equivalent trigonometric expression to show that
cos pie/3 = 1/2.

  • math -

    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 60ยบ = 1/2, just like they found
    sin pi/6 = 1/2

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