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

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0
votes
2answers
143 views

Solving equation containing ArcTan terms

IN MY EDIT I DESCRIBE HOW I GOT TO THAT EXPRESSION AND THE ORIGINAL PROBLEM. I have this expression: ...
1
vote
2answers
513 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 - 1)P(...
0
votes
1answer
46 views

How do you collect trigonometric functions in a polynomial?

I have an expression that has various forms of Sin and Cos and I want to collect them specifically so that I can make substitutions. As you can see I cannot figure out how to separate i Cos[theta] ...
0
votes
1answer
64 views

Do not understand the result I'm getting from Solve [closed]

I did Solve[k2 Cos[x] - k1 Sin[x] == 0,x] Since tangent is sin over cos, the solution must be arctan(k2/k1) But ...
4
votes
2answers
634 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 ...
1
vote
2answers
125 views

Simplifying ArcTan[Cos[u], Sin[u]]

I am trying to evaluate the following expression in Mathematica: $$ \bigg| \frac{\left(1-z^{-2}\right)^n}{\left(1-z^{-1}\right) \left(2-z^{-n}-z^{-1}\right)} \bigg|^2 $$ Here $z$ is the complex ...
1
vote
0answers
41 views

Rule/Replace/Patterns [closed]

I need help with doing this question. given: Sin[x+y] Cos[x+y+z] Define using Patterns a rule (specifically a list of 2 rules ) , the two adding rules for trigonometric functions sin (a + b )...
1
vote
1answer
83 views

NIntegrate gives two results for two forms of the same function. Which one to trust?

I am interested in evaluation the following integral numerically (since apparently there is no analytical solution) $$\int dx \,x^3 \left(e^{2 i c x }-i \text{erfi}\left(\frac{x +i c }{\sqrt{2}}\...
0
votes
1answer
78 views

Calculating the angle between the line joining two points and the x-axis [closed]

I need to calculate the angle between two points, the returned result should between $0$ to $2π$ and getAngle[point1, point2]==getAngle[point2, point1]. I have ...
-1
votes
1answer
32 views

What does mean |sin(z)|<=1? [closed]

I already know that the magnitude of sin(z) its equal to sqrt(sin^2(x)+sinh^2(y))
0
votes
2answers
260 views

Maximizing a trigonometric function

This is probably a naive question, but here it goes: I know that $$r\cos a+s\cos b+t\cos c \leq \frac{rs}{2t}+\frac{rt}{2s}+\frac{ts}{2r},$$ subject to the conditions $a+b+c=\pi$ and $r,s,t$ are ...
0
votes
2answers
56 views

Put a trigonometric equation in the form A*cos(theta)+B*sin(theta)+C=0 [closed]

eq = (Cos[Θ[t]]cf - Cos[γ1[t]] mf + Cos[γ2[t]] mf)^2/cf^2 + (Sin[Θ[t]]cf + Sin[γ1[t]] mf - Sin[γ2[t]] mf + xP1[t] - xP2[t])^2/cf^2 Can you help me to simplify and ...
0
votes
1answer
35 views

Replacement of a group of variables in trigonometric expression

I would like to make simplification of trigonometric expressions by using a replacement a group of variables. Here the equation I have to simplify : ...
3
votes
1answer
57 views

Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
0
votes
1answer
57 views

How to evaluate and simplify series expansions of long partial derivatives involving trigonometry?

I have 4 maps defined on a plane, i.e. on $\mathbb{R}^{2}$. Let's call them $F,G,H,J$. Let $(s,t) \in \mathbb{R}^{2}$. Define $F(s,t) = (f_{1}(s,t), f_{2}(s,t)).$ Likewise, in components, write $$ G(...
3
votes
1answer
99 views

Indefinite integral of nested trig functions [closed]

I tried vainly to integrate nested trig functions like Integrate[Sin[Cos[x]], x] Mathematica does not find a solution. At first I thought there was no solution, ...
1
vote
0answers
31 views

How can PowerExpand be made to evaluate the ArcTan form that takes two arguments?

Consider c = Cos[phi]; s = Sin[phi]; ArcTan[c, s] // PowerExpand ArcTan[s/c] // PowerExpand which yields ...
8
votes
2answers
131 views

Numerical solve question

Why does this work? Solve[5 Tan[t] + 9 == 0 && 0 <= t < 2 Pi , t] {{t -> π - ArcTan[9/5]}, {t -> 2 π - ArcTan[9/5]}} But this doesn't. <...
0
votes
2answers
240 views

A function generating particle-in-a-box eigenfunctions

This function sequence is defined over $\left[-\frac{L}{2},\frac{L}{2}\right]$ (all elements are valued 0 outside this interval): $$\psi_n(x)=\begin{cases}\sqrt{\frac2{L}}\sin{\left(\frac{n\pi x}{L}\...
4
votes
1answer
86 views

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 ...
1
vote
2answers
268 views

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: ...
4
votes
0answers
74 views

Why does Mathematica gives a solution which is not in the domain of the cot function? [closed]

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 $\...
4
votes
1answer
72 views

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 ...
-2
votes
1answer
83 views

Simplify a expression with cos 2x

I would like to simplify the following expression : r Cos[γ[t]] + Sqrt[l^2 - r^2/2 + 1/2 r^2 Cos[2 γ[t]]] by using the mathematical expression : ...
0
votes
1answer
49 views

Quick simplification of a fraction of 2 trigonometric equations

I would like to simplify a fraction of 2 trigonometric functions ...
1
vote
1answer
89 views

Solving trigonometric functions in Mathematica

I am new to Mathematica language and recently I had the need to solve the following equations with two variables, A and B: ...
10
votes
1answer
201 views

How does Mathematica calculate $\sin(\pi/5)$?

Consider: Sin[Pi/5] which returns: $$\sqrt{\frac58-\frac{\sqrt5}{8}}$$ Does anyone know how to figure out the trigonometric identities used by Mathematica to ...
2
votes
1answer
73 views

How to a convert a 2D vector into an angle [closed]

How do you calculate the angle between the line from the origin to a point $(x,y)$ and the horizontal axis?
13
votes
3answers
2k views

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 ...
2
votes
1answer
91 views

What function can transform A*Cos[x]+B*Sin[x] to Q*Sin[x+R] form? [duplicate]

I've tried several functions related to trigonometric transformations, namely TrigFactor, TrigExpand, ...
20
votes
2answers
4k 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 ...
1
vote
1answer
56 views

Solving a simple trigonometric equation in a range

I would like to solve a simple trigonometric equation, for example $\sin\theta=\frac{1}{2},$ but Solve gives the single solution obtained by using the inverse ...
1
vote
1answer
64 views
3
votes
0answers
90 views

Inconsistent results for symbolic trigonometric integral

I am trying to evaluate (on Mathematica v.9) the integral \begin{equation} \int_0^x [\sin (x) \sin (2 y)-\sin (2 x) \sin (y)]^t \,\mathrm{d}y, \end{equation} where $t$ is an even, positive integer. ...
8
votes
7answers
1k 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 ...
1
vote
0answers
31 views

Not reducing Trig Functions to zero [duplicate]

How do I tell Mathematica to reduce trig functions to zero when their arguments are integer multiples of pi or 2pi? I have this: ...
17
votes
3answers
1k 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.
6
votes
3answers
918 views

Replacing Tan[x] with Sin[x]/Cos[x]

Why doesn't this work? (1 - Tan[x])/(Sin[x] - Cos[x]) /. Tan[x] -> Sin[x]/Cos[x] I get back: ...
4
votes
3answers
2k views

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 ...
0
votes
1answer
45 views

Solving a trigonometric equation for all $x$ using constant coefficients

I want to find the coefficients $a$, $b$, $c$, etc. that make an equation like $a+bx=x$ true for all $x$, but for trigonometric functions of $x$. For example ...
4
votes
1answer
285 views

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]]]]] ...
1
vote
3answers
118 views

Coefficient and Addition Formula

If I type: Coefficient[Cos[x + b], Cos[x]] I get zero. But I would like Mathematica to apply: $$\cos(x+b)=\cos x\cos b-\sin x\sin b$$ Therefore the ...
2
votes
1answer
107 views

Two different results for same symbolic integral

I am trying to compute the following integral $\int_0^\infty dk \frac{e^{i k a}}{k^2}[\sin(kb)-kb\cos(kb)]$ When computing it as-is, i.e, with the code ...
21
votes
2answers
1k views

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 ...
1
vote
0answers
49 views

Write trigs in terms of Cosine only

I have a long expression having terms that go in squares like Sin[x]^2 and Sin[x/2]^2 and so on... I would like to rewrite my ...
3
votes
3answers
228 views

How can I make Mathematica trigger the simplification of ArcCos[a]+ArcCos[b]?

According to this Wikipedia subsection my guess is that I should be able to convince Mathematica to return zero when doing ...
2
votes
3answers
119 views

Adding more specific assumptions to Integrate

Let's say I would like to find a symbolic form for the integral $$\int_0^{2\pi}\sin^nx\,\mathrm{d}x$$with the added condition that $n$ is not only an integer, but an even one at that. Can this be done?...
0
votes
1answer
186 views

Why does Mathematica give this ArcSin[2] result?

The code N[ArcSin[2]] evaluates to 1.5708 − 1.31696 I but it should be undefined instead because it is on the branch ...
2
votes
2answers
295 views

Highlighting a single Period of a Trig Plot

How do I highlight a single period of a trig function say by using color and/or thickness when the graph itself extends further than just a single period? Thanks...Gregory Lane
0
votes
1answer
54 views

Using Trig functions

This is a fairly simple notation problem. I am trying to compute ArcTan of the point (5,2). I have the code: ArcTan[5,2] which outputs: ...