Arccosine function

Here we have two possible signs for p, because we have an arccosine function, which gives two possible solntions for a single argument. Thus, the phase ambiguity is actually a mathematical problem. 

Sketch graphs of the arcsine function, the arccosine function, and the arctangent function. Include only the principal values. g]... 

Fig. 17. Decryption using real-valued patterns, (a) Original image. The fingerprint image is inverted and the gray scale of each pixel is nonlinearly transformed by an arccosine function (compare it with Fig. 2(a)). (b) Encryption key, (c) real part of the encrypted pattern, (d) real part of the decryption key, and (e) decrypted image.

Wp is the weight given to the phase restraint, and / is a square well function with a width equal to the arccosine of the figure of merit (fom(h)) for each reflection. Another possible form of Exray which we call the vector residual does not use the amplitude residual at all but instead simultaneously restrains the real (A) and imaginary (B) parts of the structure factor [24]. It has the form... 

Some forms of BASIC may not have an arccosine (ACOS) function, even though they all have an arctangent function, ATAN or ATN. Perhaps this omission has come about because arccosine (and arcsine) can be expressed in terms of arctan. In fact, some BASIC manuals give the explicit formulas for computing arccosine and arcsine. 

Built-in functions and operators sqrt () - square root, abs () - absolute value, - factorial, sin() - sine, cos() - cosine, tan() - tangent, asin() - arcsine, acos () - arccosine h atan () - arctangent. It is possible to work with other functions if they have been defined before. 

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