
Square root of 2 over 2 
blargmob
Member #8,356
February 2007

I know that the sin of pi over 4 is equal to the square root of 2 over 2. But...why? How do you go from: Sin(Pi/4) to Sqrt(2)/2...
 
SiegeLord
Member #7,827
October 2006

SOHCAHTOA among others. "For in much wisdom is much grief: and he that increases knowledge increases sorrow."Ecclesiastes 1:18 
blargmob
Member #8,356
February 2007

An explanation would be cool  
SiegeLord
Member #7,827
October 2006

From that mnemonic, sin equals the length of the opposite side over the length of the hypotenuse in a right triangle. Construct a triangle with one angle equal to Pi / 4, and find what the opposite over hypotenuse is. Hint: That triangle is isosceles, so using the Pythagorean theorem is rather simple. "For in much wisdom is much grief: and he that increases knowledge increases sorrow."Ecclesiastes 1:18 
Matthew Leverton
Supreme Loser
January 1999

pi / 4 = 45 degrees. Consider the unit circle with radius=1. a and b are length 1. c is sqrt(a^2 + b^2) = sqrt(2) sin is opposite / hypotenuse = 1 / sqrt(2) = sqrt(2) / 2. 
BAF
Member #2,981
December 2002

iz dat hohmwerk 
blargmob
Member #8,356
February 2007

Matthew Leverton said: pi / 4 = 45 degrees. Consider the unit circle with radius=1. a and b are length 1. c is sqrt(a^2 + b^2) = sqrt(2) sin is opposite / hypotenuse = 1 / sqrt(2) = sqrt(2) / 2. Okay, I understood that. But how about for the sin(Pi/3)? If you use sin(Pi/3), a and b cannot equal 1 and 1 respectively because the triangle is different then for sin(Pi/4)...
 
Matthew Leverton
Supreme Loser
January 1999

blargmob
Member #8,356
February 2007

Thank you sir  
