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

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5
votes
2answers
1k views

Solving a trig equation

I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ? ...
11
votes
1answer
1k views

Persistence length of a polymer chain

I'm trying to calculate the persistence length (Lp) of a polymer chain using Mathematica. The first and simplest method is to compare the EuclideanDistance between ...
13
votes
2answers
582 views

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.
7
votes
4answers
2k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
0
votes
1answer
254 views

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 ...
22
votes
3answers
2k views

How to find the period of an arbitrary mathematical function?

Is there a function to find the period of an arbitrary (possibly complex) function in Mathematica?
10
votes
2answers
2k views

Why doesn't Mathematica expand Cos[x]^3 Sin[x]^2?

I found some examples of Mathematica's commands usage in an old manual but the program gives me different result than expected ...
4
votes
2answers
1k views

ArcTan expressed as a radian fraction?

This type of answer is what I'm looking for: In[58]:= ArcTan @ 1 Out[58]= π/4 This is what mathematica gives me: ...
6
votes
5answers
717 views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

Consider the function f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the first derivative. We have to ...
7
votes
1answer
4k views

Extract real part of a complex expression better than Re does

I have a complex expression with real positive variables only. Mathematica Input Style: ...
13
votes
2answers
47k views

Generate a Unit Circle Trigonometry

Struggling often with Trigonometry I would like to have some code to generate this Unit Circle Trigonometry. Would be of great help when I need to transform some data :
11
votes
1answer
10k views

How to express trigonometric equation in terms of of given trigonometric function?

How can I express a trigonometric equation / identity in terms of a given trigonometric function? using following trigonometric identities ...