I was afraid of this: you have to check the labels of the variables you use.
In the laste expression in Prime, there are two different p's, the p as an argument to f() is labelled as a 'variable',
the other two p's (the one next to d, and the p to solve for) are labelled 'automatic' shown as (-).
make sure they are all labelled the same, and it should work.
Success!
Luc
Do you now what's the difference between the 3 solutions?
Usually, we should have some specific limitation or range for each solution? but mathcad didn't specify these ranges, is there any way to look into these ranges?
Do you now what's the difference between the 3 solutions?
Usually, we should have some specific limitation or range for each solution? but mathcad didn't specify these ranges, is there any way to look into these ranges?
To find that out, you'll have to look at the derivatives. For example, the derivative to p is:
This one is 0:
1. When p=0, becasue then sin(p)=0
2. When M*cos(theta)*cos(p)=cos(s), that is when cos(p)=cos(s)/(M*cos(theta)), thus when:
arcos(cos(p))=p=arcos(cos(s)/(M*cos(theta))). Since the cosine is a periodic function, there's an infinite number of solutions, so this happens for both positive and negative values of p with the same magnitude. The first set (closest to 0) is found and usually given by Mathcad. If you want all, you can add ",all" to the symbolic solve command.
What Fricas (The new symbolic solver) did was give you only the (first) positive solutions...
Success!
Luc
Trying to explain why muPad also adds -acos(...) to its solution and why this is correct in my opinion.
In mathematics arccos is NOT the inverse of the cos function, but rather is the inverse limited to the range from 0 to pi. The inverse of the cos function would have an infinity number of values for every single argument and therefore is not a function in the mathematical definition.
To solve the equation cos(x)=C requires x = arccos(C) but also x = - arccos(C) OR x = 2 pi - arccos(C). And of course you may add any integer multiple of 2 pi to any of these two "main" solutions.
friCAS seems to have its own interpretation and I definitely prefer the correct answers of muPad:
