Ah, ok. So also your "I'm not trying to nitpick" makes more sense ;-)
To summarize: You can have a table for 0 to 45 degrees for sine and another in the same range for cosine, instead of a table for 0 to 90 degrees of sine (or else cosine). In fact that makes no difference in the amount of values, right you are. I should have emphasized in my first post to this thread that I meant one single table for both sine and cosine.
how many radians in 360deg?
Quote:Original post by deavik
/edit: Theoretically, it's possible to drive a lookup using just the values of sin(0) through sin(45) and using the relation cos2(x) = 1 - sin2(x) to get the values of cos 0 to cos 45. After that use the complementary angle relation and get values of sin and cos for all x 0->90. From there, it's simple. But this approach requires more computing power, using a square and a square root, and the little more memory for the lookup table (0->90) is more practical.
Yeah, that is really theoretical, since the effort of computing especially sqrt is in its order comparable to computing the sine directly. However, if not thinking about alternative solutions also better solutions will not be found.
Does anyone know why the number of radians in a circle is 2*pi, rather than just pi? Is there a mathematical reason for it? I'd have thought having pi radians in a circle would be simpler.
Quote:Original post by Bezben
Does anyone know why the number of radians in a circle is 2*pi, rather than just pi? Is there a mathematical reason for it? I'd have thought having pi radians in a circle would be simpler.
Because the circumference of a circle with radius one, the unit circle in other words, is 2*Pi. What this means is illustrated here; an arc of V radians in a unit circle is V units long.
Perhaps it is because pi was first determined using the diameter, and not using the radius:
U := 2 * pi * r = pi * d
So it may have come to the magic pi. For the rest of the story (say the definition of radians) see the Brother Bob's post above.
[Edited by - haegarr on November 30, 2005 11:05:52 AM]
U := 2 * pi * r = pi * d
So it may have come to the magic pi. For the rest of the story (say the definition of radians) see the Brother Bob's post above.
[Edited by - haegarr on November 30, 2005 11:05:52 AM]
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