Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.
21
votes
3answers
1k 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?
17
votes
4answers
455 views
How do I introduce a new variable in a trigonometric equation?
I have the trigonometric equation
\begin{equation*}
\sin^8 x + 2\cos^8 x -\dfrac{1}{2}\cos^2 2x + 4\sin^2 x= 0.
\end{equation*}
By putting $t = \cos 2x$, I have
\begin{equation*}
\dfrac{3}{16} t^4+ ...
16
votes
2answers
505 views
ArcTan[0,0] numeric approximation
I've noticed that the numeric approximation of ArcTan is a bit different from the symbolic one.
If I write
ArcTan[0,0]
I ...
15
votes
1answer
294 views
Speeding up trigonometric integral
Context
On a possible non trivial toric topology for the Universe (nothing less!).
Problem
I would like to carry out the following integral for $\ell=2,4\cdots 20$.
$$\int _0^{\pi }\int _0^{2 \pi ...
11
votes
1answer
5k 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
...
10
votes
2answers
1k 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
...
10
votes
2answers
323 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.
10
votes
0answers
594 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 ...
8
votes
2answers
6k 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 :
7
votes
4answers
911 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'' ...
7
votes
2answers
817 views
How to expand tan(x+y) as normal form?
TrigExpand@Tan[x + y]
gives
$\frac{\sin (x) \cos (y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}+\frac{\cos (x) \sin(y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}$
but I ...
7
votes
1answer
2k 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:
...
6
votes
5answers
570 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 ...
5
votes
4answers
385 views
How to transform the result of this integral into powers of $\sin\,x$?
I want to calculate the integral
$I = \displaystyle\int{\cos ^5 x\, \mathrm dx}$. Using the variable $t = \sin x$, I get
$$I = \sin x - \frac{2}{3}\sin^3 x + \frac{1}{5}\sin^5 x + C.$$
With ...
5
votes
2answers
556 views
Solving a trig equation
I am trying to find an explicit solution to a trigonometric equation. It is running for a long time and I didn't get any result, but Maple solves it quickly. Why ?
...
4
votes
2answers
651 views
How do I work with Root objects?
I want to solve the trigonometric equation :
$$(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 ...
4
votes
2answers
591 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:
...
4
votes
4answers
147 views
Arcs of rotation for angles
How can I draw trigonometric angles of any radian measure associated with the unit circle, complete with the x-axis and y-axis?
How can I draw arcs of rotation inside positive or negative angles?
Is ...
4
votes
2answers
210 views
Both Sin[x]==0 && Cos[x]==0 as a solution
If I do
FullSimplify[Reduce[Sin[p1] == 0 && Cos[p1] == 0, Reals]]
I get
Cos[p1] == 0 && Sin[p1] == 0
...
4
votes
1answer
248 views
Solving trig identities in specific terms
How would you solve a problem like "write csc(x) in terms of sec(x)" in Mathematica? The best I can get is "True."
http://math.stackexchange.com/questions/167935/write-cscx-in-terms-of-secx
I'm ...
4
votes
1answer
106 views
How to check if a given expression is an “explicit algebraic number”?
The documentation for PossibleZeroQ says:
With the setting Method...
3
votes
3answers
136 views
How to extract phase angle from sinusoid
I'm doing some electric circuit calcualtions and I'm trying to get the phasor representation of some arbitrary function of Sin or Cos. Could be complex like:
...
3
votes
2answers
272 views
Evaluating the integral of $\cos (\theta )\cos\left[\tan ^{-1}\left(\frac{a^2 \tan (\phi )}{b^2}\right)\right]$
I am trying to evalute the following integral:
Integrate[Cos[θ] Cos[ArcTan[a^2/b^2 Tan[φ]]], {φ, 0, 2π}]
I know that for $a=b$ I should get 0 out of the integral ...
2
votes
3answers
67 views
Problem with simplifying Sinc function
$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals;
These work:
...
2
votes
1answer
86 views
Problem with Sinc[x] function and rounding
I seem to be having some trouble with the Sinc[x] function, and I think it's due to rounding, but I'm not sure.
The code is below, with relevant constants:
...
2
votes
2answers
206 views
How do I get the solutions of a cubic equation in trigonometric form?
I know $x^3-3 x+1=0$ has three roots that can be expressed in trigonometric form:
$\{2\sin(10^\circ),\,-2\cos(20^\circ),\,2\cos(40^\circ)\}$.
How can I get this result with Mathematica?
2
votes
1answer
111 views
Discard functions with wrong symmetry?
I have functions of x, where x is the polar angle of spherical coordinates, i.e. ...
1
vote
1answer
116 views
How can I get Mathematica to write Log instead of ArcTan?
ArcTan really bothers me, so is there a way to make Mathematica write Logarithm instead of ...
1
vote
1answer
127 views
How can I factor my trigonometric equation?
The equation
$$3\sin^2 x - 3\cos x -6\sin x + 2\sin 2x + 3=0$$
has a solution $x = 0$. That means it has a factor of $\cos x - 1$. I tried to write the given equation has the form
$$(\cos x - ...
0
votes
2answers
125 views
Sum of roots of a trigonometric equation
The equation $$ \sin x + \sqrt{3} \cos x = 1,$$
where $x \in [-2\pi, 2\pi]$ has four roots $-\dfrac{3\pi}{2}$, $\dfrac{\pi}{2}$, $\dfrac{\pi}{2}$ and $\dfrac{11\pi}{6}$. Sum of roots of the given ...
0
votes
1answer
196 views
Get Mathematica to simplify $\cosh(i x)$
I want Mathematica to simplify Cosh[I x] to Cos[x] if I tell Mathematica that x is Real.
I ...
0
votes
1answer
72 views
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 ...
0
votes
2answers
189 views
Simplifying a trigonometric equation to obtain specific terms
When I try to solve the non-homogeneous differential equation
...
0
votes
1answer
84 views
Non solutions returned by NSolve. And why does it return both phi and Cos[phi]?
Similarly to this thread
NSolve gives additional solutions that don't satisfy the equations!
NSolve returns "spurious" solutions, even increasing the working precision
...
0
votes
1answer
102 views
Wolfram Alpha's Mysterious Trig Abilities [closed]
This is a very straight-forward question:
I'm trying to simplify [sin(2pi*t +pi/4) + sin(2pi*t -pi/4)], and failing at it:
...
0
votes
1answer
32 views
Plot not displaying [duplicate]
I'm trying to perform a basic plot to show that two equations align, but I'm not getting any results.
Plot[{[Pi]*Cos (3 x - [Pi]), [Pi] * Sin (3*[Pi] - 3 x)}, {x, -3 [Pi], 3 [Pi]}]
To me this seems ...
