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

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3
votes
3answers
477 views

How to solve the equation $A \sin x + B \cos x = 0$ for all $x$?

I have the equation: $A \sin x + B \cos[x] = 0$ that should be satisfied for all the $x$. Of course, the solution is obvious: $A=B=0$, but I need Mathematica to resolve it automatically because this ...
3
votes
3answers
218 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 ...
3
votes
3answers
241 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
3
votes
1answer
168 views

Sum to Product Trig Identities

All, I was enjoying sum to product trig identities in Mathematica, smiling that it was going well, producing the same answers trig students get by hand. ...
3
votes
4answers
336 views

Redefine ArcCot to be inverse of range [0, Pi]

Mathematica implements ArcCot function as an inverse to Cot on range [-Pi/2, Pi/2]. I ...
3
votes
1answer
55 views

Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
3
votes
3answers
476 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
186 views

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 ...
3
votes
1answer
519 views

Mathematica takes too long to solve this

I have the following system of equations: ...
3
votes
1answer
96 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, ...
3
votes
0answers
89 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. ...
3
votes
0answers
118 views

Why does Mathematica show 4095/4096 terms in TrigExpand?

Clear[x, n]; expr = Cos[x]^(n - 2) (1 - Cos[x]^2 + Sin[x]); r=TrigExpand[expr] Where do those 4095/4096 comes from? It is correct, but it seems very strange ...
2
votes
2answers
293 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
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?
2
votes
3answers
621 views

Problem with simplifying Sinc function

$Assumptions = x ∈ Reals && y ∈ Reals && a ∈ Reals && b ∈ Reals; These work: ...
2
votes
1answer
51 views

TrigExpand-ing too far

Something simple: I'd like TrigExpand[Sin[3n-3]] to return Sin[3n]Cos[3]-Cos[3n]Sin[3] instead of ...
2
votes
2answers
655 views

Is it possible to simplify a trigonometric expression only in terms of $\cos (u)$ OR $\sin (u)$?

I want to expand the following expression into powers of $\cos(u)$ only: a1 + a2 Cos[2 u] + a3 Cos[4 u] + a4 Cos[6 u] The answer that I want (and which I found ...
2
votes
3answers
785 views

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. ...
2
votes
2answers
182 views

Trigonometry expansion of a product

The following command does what I want: ...
2
votes
2answers
181 views

Showing steps for TrigExpand

If I enter a double equal sign and the following in Mathematica 10: == integrate 1/(1+x^4) Then wolfram alpha allows me to select a Step-by-step solution, which ...
2
votes
1answer
673 views

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 ...
2
votes
1answer
418 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
1answer
90 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, ...
2
votes
1answer
107 views

Simplify trigonometric expression

Mathematica correctly simplifies the following expression: ...
2
votes
1answer
996 views

Mathematica's ArcTan function [duplicate]

I'm trying to calculate the angle made by a vector from two vector components but am having some trouble. The x-component has a magnitude of -2.7388321862151737*^10 and the y-component has a magnitude ...
2
votes
2answers
557 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
373 views
2
votes
1answer
189 views

Discard functions with wrong symmetry?

I have functions of x, where x is the polar angle of spherical coordinates, i.e. ...
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 ...
2
votes
3answers
118 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 ...
2
votes
1answer
608 views

Prevent FullSimplify from converting trigonometric expressions to exponential

There's an option for FullSimplify, which is Trig, and with it I could prevent a trigonometric identities from being used. I'm ...
2
votes
2answers
436 views

How to change the form $A\cos \omega t + B\sin \omega t$ into the form $\sqrt{A^2+B^2}\cos(\omega t-\phi)$ [duplicate]

I'm preparing notes for teaching next week's class in differential equations. My hand calculation solution of $$y''+192y=0, y(0)=1/6, y'(0)=-1$$ is $$y=\frac16\cos 8\sqrt3 t-\frac{\sqrt3}{24}\sin ...
2
votes
0answers
86 views

TrigExpand Idiosyncracies

TrigExpand[Sin[x]^2 Log[y]] returns sin^2(x) log(y), as one would expect. However, ...
1
vote
4answers
3k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
1
vote
3answers
413 views

Solve simple trig equation

I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to ...
1
vote
2answers
259 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: ...
1
vote
2answers
175 views

how can tangent half angle substitution be done in Mathematica?

Is it possible to replace sine and cosine in terms of tangent half-angles and again the tangent half-angles by a variable say t?
1
vote
2answers
123 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
1answer
364 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 ...
1
vote
3answers
117 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 ...
1
vote
2answers
170 views

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: ...
1
vote
2answers
109 views

Abs[Sin[4a]] not equal to 2Sin[2a]Abs[Cos[2a]] for a in [0,\pi/2]

I have a long expression which is not fully simplified because Abs[Sin[4a]] is considered different from 2Sin[2a]Abs[Cos[2a]] ...
1
vote
1answer
312 views

Get Cos[2 x] in “Solve”

My goal is to get an analytical solution of x ( $\lambda$ in the problem), when $\epsilon$ (f[x] in the problem) is maximum (use inverse form). I found that if I can use trigonometric identity ...
1
vote
1answer
1k 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
55 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
87 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: ...
1
vote
1answer
62 views

3D-plots of Complex-parametered trig-functions returns empty plot

I first tried to plot a parametric equation as follows; ...
1
vote
1answer
242 views

How to solve trigonometric equations

I have the following problem: I need to solve the equation: $$\frac{\cos\left(x\right)}{x^6} - \frac{6 \sin\left(x\right)}{x^7}==0$$ and I don't really remember how to do it symbolically. Some help ...
1
vote
2answers
94 views

Convert imaginary exponentials to goniometric expressions?

Can I force Mathematica to re-express something like $$\left\{\frac{1}{2}i\left(\frac{1}{16} e^{-2 i (\alpha (1)+4 \alpha (2))} \left(-1+e^{8 i \alpha (2)}\right) \text{d$\alpha $}(1) \left(2 \left(2 ...
1
vote
1answer
82 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 ...