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

???

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"No amount of prayer would have produced the computers you use to spread your nonsense." Arthur Kalliokoski

SiegeLord
Member #7,827
October 2006
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SOHCAHTOA among others.

"For in much wisdom is much grief: and he that increases knowledge increases sorrow."-Ecclesiastes 1:18
[SiegeLord's Abode][Codes]:[DAllegro5]:[RustAllegro]

blargmob
Member #8,356
February 2007
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An explanation would be cool :-/

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"No amount of prayer would have produced the computers you use to spread your nonsense." Arthur Kalliokoski

SiegeLord
Member #7,827
October 2006
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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
[SiegeLord's Abode][Codes]:[DAllegro5]:[RustAllegro]

Matthew Leverton
Supreme Loser
January 1999
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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
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iz dat hohmwerk ???

blargmob
Member #8,356
February 2007
avatar

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)...

???

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"No amount of prayer would have produced the computers you use to spread your nonsense." Arthur Kalliokoski

Matthew Leverton
Supreme Loser
January 1999
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blargmob
Member #8,356
February 2007
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Thank you sir :D

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"No amount of prayer would have produced the computers you use to spread your nonsense." Arthur Kalliokoski

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