# Tagged Questions

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

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### 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?
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### 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 ...
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### Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
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### Behavior of ArcTan when two zeros are given as arguments

I've noticed that the numeric approximation of ArcTan is a bit different from the symbolic one. If I write ArcTan[0,0] I ...
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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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### 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+ \...
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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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### 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 :
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### Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
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### Combining Cos[ ] terms

A function that is the sum of two Cosine terms of the same frequency x[t_] := a1 Cos[w0 t + b1] + a2 Cos[w0 t + b2]; can be simplified to a single ...
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### How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
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### 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 ...
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### 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 ? ...
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### Trigonometric simplification

How can I simplify 1/2 (Sqrt[3] Cos[x] - Sin[x]) in order to get Cos[x + Pi/6] on Mathematica? I saw that Wolfram|Alpha lists ...
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### 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: ...
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### Simplifying a trigonometric expression

I'm sure this has been addressed before, but I can't find it! I want Mathematica to simplify Sqrt[1 - Sin[π/6 - θ]^2] to ...
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### Eliminate 3 Variable from 4 Equations

I am trying to use Mathematica to Eliminate 3 following variable from 4 equations. Any clue or link to similar solved problem is highly appreciated: ...
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### Simplify $\tan(\arctan(a) - \arctan(b))$

I want to simplify the expression $\tan(\arctan(a) - \arctan(b))$ to $\tfrac{a-b}{1+a\cdot b}$ (if $b \neq - \tfrac{1}{a}$). Right now, the output of ...
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### Why Refine does not simplify Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] to $(-1)^{i+j+k}$?

I am obtaining in Mathematica: Cos[2*Pi*FractionalPart[1/2*(i + j + k)]] We know that for $i, j, k$ being positive integers this expression after simplification ...
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### Infinite expression encountered when simplifying ArcTan sums although the result is finite

If I attempt to simplify the sum ArcTan[1/x] + ArcTan[x] with ArcTan[ Simplify[ TrigExpand[ Tan[ ArcTan[1/x] + ArcTan[x]]]]] ...
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### Mathematica not recognising closed forms as specific values

I have a Mathematica program that outputs a piecewise function, and some parts of the expression are not being recognised as specific numbers when using FullSimplify...
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### ArcTan[z] and ArcTan[x,y], Restriction and Conversion

In Mathematica there are two different forms for the arctangent (inverse tangent), namely ArcTan[x,y] which gives the arc tangent of $y/x$, taking into account ...
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### 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 ...
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### 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 ...
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### How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method...
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### Strange behavior of ArcTan [duplicate]

I've noticed a strange behavior of Mathematica's ArcTan function with two arguments. If both arguments are 0 or ...
### 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 ...
I've tried to solve the equation $\cot \theta = 2 \cot 2\theta$ with the command Reduce and Mathematica gave $\theta = n\pi$ as solution, with $n$ an integer. But \$\...