arc sine

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arc sine

[¦ärk ¦sīn]
(mathematics)
Also known as antisine; inverse sine.
For a number x, any angle whose sine equals x.
For a number x, the angle between -π/2 radians and π/2 radians whose sine equals x ; it is the value at x of the inverse of the restriction of the sine function to the interval between -π/2 and π/2.
References in periodicals archive ?
Coefficients for curve modeling are computed using probability distribution functions: polynomials, power functions, sinus, cosine, tangent, cotangent, logarithm, exponent or arcsin, arccos, arctan, arcctg.
If the variance and mean of X and Y are the same (and they are usually close here), then M/1000 is equivalent to the standard correlation coefficient r, except that the arcsin transformation (applied to a measure of Mielke 1991) means that the deviation from unity asymptotes to the square root of mse, rather than mse itself.
The arcsin [square root of x] transformation was used to normalize the fraction of cells in the S phase of the cell cycle, fraction of cells in the G2-M phases of the cell cycle, and RSG1.
[[phi].sub.1] = [pi] + arcsin [[absolute value of [GAMMA]].sub.0]/[[absolute value of [GAMMA]] - [[beta].sub.0], [[phi].sub.2] = 2[pi] - arcsin [[absolute value of [GAMMA]].sub.0]/[[absolute value of [GAMMA]] - [[beta].sub.0].
[alpha](i) = arcsin [2 (dx(i) - [dx.sub.-90]/[dx.sub.+90] - [dx.sub.-90] - 0.5)], (1)
[DELTA][phi] = 2 x arcsin [[a.sub.z]/[2 x [R.sub.v] x cos [[alpha].sub.v]]] (13)
7: [F.sub.6,23] = 1.08, P = 0.41, with arcsin transformation).
Mortality of mosquito larvae was analyzed by ANOVA, previous arcsin data transformation, to detect significant differences among treatments and controls.
Demographic data were tested for normality, and transformed when necessary; proportions were transformed by arcsin [check]p (Zar, 1999).
d = 2R X arcsin ([square root of [haversin([DELTA][PHI]) + cos [[phi].sub.1]cos [[phi].sub.2]haversin([DELTA][phi])]])
Analyses.--I compared the among-year differences of A) percent daily loss in mass while nest-guarding (arcsin transformed) and B) percent daily gain in mass subsequent to release (arcsin transformed) with one-way ANOVAs, using proportional values to accommodate for the differences in size of the spiders.
and rewriting the "arcsin" as an "arctan" form, we obtain the new integral