Arc SOHCAHTOA method

[Albert Chan]

Inspired from pi day thread, I discovered a great mnemonic for arc-trig function



asinq(x) = asin(√x)
acosq(x) = acos(√x)
atanq(x) = atan(Vx)

Above definition remove the annoying square roots.
Example, from asin(x) = acos(V(1-x²)), we have:

asinq(x) = acosq(1-x) = atanq(x/(1-x))                → Triangle O, A, H = x, 1-x, 1

asinq and acosq now appeared complementary, O/H + A/H = 1, or O+A = H

Or, relative to atanq(x):

asinq(x/(1+x)) = acosq(1/(1+x)) = atanq(x)       → Triangle O, A, H = x, 1, 1+x

We can use the relation to build truly compact code.
For example, to get sqrt(x^2/(1+x^2)), we only need 2 keys: ATAN SIN