Homework Help Forum: math

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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