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Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.

18
votes
Mathematica auto simplifies simple trig expressions like these, but you can turn off this setting via SystemOptions: SetSystemOptions["SimplificationOptions" -> "AutosimplifyTrigs" -> False]; Now w …
answered Dec 13 '15 by Chip Hurst
13
votes
Here's two possibilities: Simplify[TrigExpand[Tan[ArcTan[a] - ArcTan[b]]]] (a - b)/(1 + a b) FullSimplify[Tan[ArcTan[a] - ArcTan[b]], ComplexityFunction -> (LeafCount[#] + 1000 Count[#, ArcT …
answered Feb 26 '16 by Chip Hurst
6
votes
We can take the Floor and Ceiling from Carl's answer and expand them out: PiecewiseExpand[ PowerExpand[ArcSin[Sin[x]], Assumptions -> x ∈ Reals], -π/2 < x < 3π/2 ] Edit As it turns out, we …
answered Nov 6 '18 by Chip Hurst
8
votes
One idea is to extend the domain with a piecewise function by taking limits at singularities. ExtendFunctionDomain[expr_, vars_] := Module[{domain, antidomain, locassums, lims}, domain = FunctionDo …
answered May 20 '15 by Chip Hurst
4
votes
Eliminating the trigonometric terms work in this case: expr = 4 n^2 Cos[Φ]^2 HypergeometricPFQ[{-n,1-n/2-1/2 n Cos[2 Φ],1-n/2- 1/2 n Cos[2 Φ]},{-n Cos[Φ]^2,-n Cos[Φ]^2},-Cot[Φ]^2] Sin[Φ]^(-2+2 n); …
answered Apr 24 by Chip Hurst
21
votes
Disclaimer: This is not a full answer, but perhaps it's a start. From an algebraic stand point this seems like a very hard problem. I attacked it with a more brute force approach. I guess a basis and …
answered Jan 2 '15 by Chip Hurst
2
votes
I think I have solved this ODE (I didn't verify the solution). The problem with DSolve is Integrate was not terminating for this inhomogeneous equation. So what I did was solve the homogeneous equati …
answered Nov 19 '14 by Chip Hurst
1
vote
Not sure if this will help, but you can transform your ODE to have rational coefficients by subbing $t = \cos x$, which gives $k'(x)=-\sqrt{1-t^2} k'(t), \quad k''(x)=(1-t^2)k''(t)-t k'(t), \;\; \tex …
answered Apr 22 '14 by Chip Hurst
4
votes
Similar to the answer here, we can use PowerExpand. PowerExpand[ArcTan[Cot[a]], Assumptions -> 0 < a < π/2] π/2 - a In fact an almost identical example appears in the PowerExpand ref page here. …
answered Feb 11 by Chip Hurst