Jan-23-2024, 06:51 AM
(Jan-22-2024, 03:44 AM)charlesrkiss Wrote: I went to a random calculator website: https://math.tools/calculator/trignometry/asin
From there I found similar results and created a table of the values (see image below):
I know the circle looks pretty flat (linear), when the angle is very small, but the radian numbers are just spooking me (the zeros and sixes).
On the other hand, the values in the "Degrees" column in the table do not look so bad — they change in a way that does not appear as weird. Maybe degrees are a more comforting unit to work with in this case (and they are about 60 times smaller than radians).
The values look fine to me. Some
Assuming is in radian, x is between -1 and 1, then
asin(x) can be approximated by x + (x**3 / 6) + (3 * x**5 / 40) + .... Let's try it with x =0.01.
asin(0.01) = 0.01 + (0.000001/6) + (3 *0.0000000001/40)
which becomes
asin(0.01) = 0.01 + 0.000000166666666... + 0.0000000000075
or
0.010000166674166668
Sorry about the lack of formatting and terseness.
