solve(sin(2*x)=-1,x)|0< x <2pi
ITentatively think it is Tinspire's way of naming a closed variable
that has to be a particular subset of integers.
It's closed and not open because, unlike x and y, it's value is
independant and fixed.
It's a variable because, unlike pi, it's value, though independant is
not known.
It's "n" because, unlike other closed variables a, b, and c, it's
fixed value has to be an integer.
It has a number after it because each different n represents a unique
subset of integers, like the n's in the generalized polynomial formula
that represent "the specific integer equal to the number of terms" or
on the cosine example and other trig functions "any integer" (where
the subset is equivalent to the full set.
The specific limitation on the set of possible integers is not
disclosed by Tinspire, because that would have been hard to write the
code for, so TI gave up before it got there during product
development.
Right?
it
it has to be an integer, unlike open variables a and b
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There are infinitely many solutions to the equation sin(x)=0. Each
multiple of pi is a solution. Without the calculator, we would write
all these infinitely many solutions using the single closed form n*pi
where n can be any one of the integers 0, plus or minus 1, plus or
minus 2, plus or minus 3,....... The ellipsis indicate that the list
is infinite. When the Nspire solves this or any problem in which
there can be infinitely many solutions, the calculator simply writes
the single closed form n*pi to indicate that any one of the integers
can be substituted for n in order to obtain a particular solution.
The calculator needs to distinguish the arbitrary constants from one
another for several reasons. The most important in my mind occurs
when a solution needs two or more such constants to completely specify
the solution. The best example I can think of for this case is the
solution of differential equations. For example, a fourth order
differential equation requires three arbitrary constants to completely
specify all the solutions. The Nspire CAS solution would include c1
and c2 and c3 as arbitrary constants in the solution. Of course the
increments would vary in each calculator depending on how many had
been used in the solutions of previous equations in the same problem
in the .tns document. Try this for yourself using the very nice
linear algebra and differential equation library that is now included
with the OS. Hope this helps clear your confusion.
Wayne
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