arcsin

(3.17) meas D([r.sup.n], b) [greater than or equal to] 4/[sigma] + 2[epsilon] arcsin [square root of ([delta]/2)] - [epsilon].

Bars with the same letter are not significantly different (ANOVA on arcsin [(p).sup.1/2], followed by the Ryan-Einot-Gabriel-Welsh (REGW) multiple Q test, a = 0.05).

M = (2/[pi]) arcsin {1 - mse/[[V.sub.x] + [V.sub.y] + [([G.sub.x] - [G.sub.y]).sup.2]]} x 1000,

A control model used temperature, SL, arcsin [square root of x]-transformed fraction of cells in the S phase, and arcsin [square root of x]-transformed fraction of cells in the G2/M phases; and a test model added arcsin [square root of x]-transformed RSG1 to the covariates used in the control model (n=158).

For [[absolute value of [GAMMA]] > [[absolute value of [GAMMA]].sub.0], the extraneous root [[absolute value of [GAMMA]].sub.ext] will be smaller than [[absolute value of [GAMMA]] if sin ([psi] + [[beta].sub.0]) < -[[absolute value of [GAMMA]].sub.0]/[[absolute value of [GAMMA]] where [[beta].sub.0] = arcsin [[absolute value of [GAMMA]].sub.0], and thus the reflection coefficient will be given by [[absolute value of [GAMMA]].sub.1] if sin ([psi] + [[beta].sub.0]) < - [[absolute value of [GAMMA]].sub.0]/[[absolute value of [GAMMA]], otherwise it will be given by [[absolute value of [GAMMA]].sub.2].

A scaling with the calibration data of the DVC was then performed, and an arcsin function was applied to convert the raw data into angles:

For h > [R.sub.k]; [[psi].sub.max] = 90[degrees] + arcsin [[h - [R.sub.k]]/[R.sub.k]].

7: [F.sub.9,88] = 6.18, P < 0.001, with arcsin transformation).

[[phi].sub.i] = [pi] - arcsin (([V.sub.i](0) - [N.sub.i]) / [M.sub.i]) (31)

[[THETA].sub.PQ(perm)] = arcsin d[THETA]xs/[rho]xdN, (5)

sin [theta]/2 = [square root of 1 - cos[theta]/2] [??] [theta] = 2 arcsin [square root of 1 - cos[theta]/2]

[[OMEGA]'.sub.c](s [member of] [c - 2, c + 2]) = 2/[pi] arcsin (s + c/2[square root of 1 + sc] ; [OMEGA]'(s [member of] [-2, 2]) = 2/[pi] arcsin (s/2).

[H.sub.1] [[eta].sub.i] = [([integral].sup.1.sub.0] [H.sub.i](arcsin)(z))dz).sup.-1] [H.sup.1] [[eta].sup.1] = 38.119 [H.sup.2,1] [[eta].sup.2,1] = 48.179 [H.sup.2,2] [[eta].sup.2,2] = 48.179 [H.sup.3,1] [[eta].sup.3,1] = 171.187 [H.sup.3,2] [[eta].sup.3,2] = 171.187 [H.sup.4,1] [[eta].sup.4,1] = 25.856 [H.sup.4,2] [[eta].sup.4,2] = 25.856 [H.sup.5] [[eta].sup.5] = 114.825 Table 2.