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matlabsqrt

Double sqrt solution in Matlab?

I would like to know how can I get both the positive and the negative solution from a sqrt in Matlab.

For example if I have:

sin(a) = sqrt(1-cos(a)^2);
Solution

  • MATLAB (and every other programming language that I know of) only returns the principal square root of x when calling sqrt(x) or equivalent.

    How you'd write the square root of x mathematically, is

    s = ±√x

    which is just a shorthand for writing the whole solution set

    s = {+√x -√x}

    In MATLAB, you'd write it the same as this last case, but with slightly different syntax, 

    s = [+sqrt(x) -sqrt(x)]

    which can be computed more efficiently if you "factor out" the sqrt:

    s = sqrt(x) * [1 -1]

    So, for your case, 

    s = sqrt(1-cos(a)^2) * [1 -1]

    or, if you so desire, 

    s = sin(acos(a)) * [1 -1]

    which is a tad slower, but perhaps more readable (and actually a bit more accurate as well).

    Now of course, if you can somehow find the components whose quotient results in the value of your cosine, then you wouldn't have to deal with all this messy business of course....