Why do the sine values for 0, π/6, π/4, π/3, and π/2 output in the patterned sqrt(0)/2, sqrt(1)/2, sqrt(2)/2, sqrt(3)/2, and sqrt(4)/2? Is this just mere coincidence, or is there something more to this pattern?

Question

Why do the sine values for 0, π/6, π/4, π/3, and π/2 output in the patterned sqrt(0)/2, sqrt(1)/2, sqrt(2)/2, sqrt(3)/2, and sqrt(4)/2?  Is this just mere coincidence, or is there something more to this pattern?

kira_yamato · Answer

For π/4, you can have a right angled isosceles triangle with the equal sides being 1 cm each. Use Pythagorean Theorem to find the length of the hypotenuse, which is sqrt (2).
For a diagram, please look at the attached file. Please note that the diagram is in degree, so you have to use the conversion 180˚ = π radians.

anonymous · Answer

I know how they are calculated.  I am just interested in finding out more as to why this pattern exists.

kira_yamato · Answer

It's due to the sine curve.

kira_yamato · Answer

and Pythagorean Theorem.

anonymous · Answer

Yes, I know, but that doesn't explain why there is a PATTERN, as opposed to more seemingly arbitrary values.