# Tagged Questions

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

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### How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
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### Mathematica Sec and Csc

How can I prevent Mathematica from using the "old fashioned" functions "Sec" and "Csc"? In Germany these functions are "old fashioned" as they are not taught anymore at school.
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### Avoid trigonometric simplifications?

When evaluating the expression Sinh[x]^2 + Cosh[x]^2 // FullSimplify I get Cosh[2 x] That is indeed a simplification, but ...
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### How to make Mathematica simplify $\cos[(i + j + k)\pi]$ to $(-1)^{i+j+k}$?

We know that: $$\cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k}$$ for $i, j, k$ being positive integers. In Mathematica I've tried: ...
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### Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...
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### TrigExpand Idiosyncracies

TrigExpand[Sin[x]^2 Log[y]] returns sin^2(x) log(y), as one would expect. However, ...
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### DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
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### Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
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### Find the explicit solution of the integral

I want to calculate the integral: assuming that we are familiar with the relation: The answer should be: The code that I've used is the following: ...
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### Force Mathematica to simplify an ArcTan[]?

I understand that there are many solutions that will produce the same arctangent, nevertheless I really need a simplification: ...
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ArcTan really bothers me, so is there a way to make Mathematica write Logarithm instead of ...
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### Get Mathematica to simplify $\cosh(i x)$ [closed]

I want Mathematica to simplify Cosh[I x] to Cos[x] if I tell Mathematica that x is Real. I ...
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### Find *all* numerical solutions to cosine based equality

To help with http://astronomy.stackexchange.com/questions/11456/ I'm trying to find all numerical solutions to: 5.20427*Sin[0.529699*t] == Sin[2*Pi*t] Since the period of the first function is ...