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

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2
votes
2answers
162 views

Trigonometry expansion of a product

The following command does what I want: ...
2
votes
1answer
519 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
337 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
386 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
171 views

Discard functions with wrong symmetry?

I have functions of x, where x is the polar angle of spherical coordinates, i.e. ...
2
votes
2answers
150 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
2answers
100 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
0answers
78 views

TrigExpand Idiosyncracies

TrigExpand[Sin[x]^2 Log[y]] returns sin^2(x) log(y), as one would expect. However, ...
1
vote
4answers
2k 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
2answers
205 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
1
vote
2answers
61 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
259 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
585 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
43 views

How to reduce trigonometric expressions under special conditions

For the following problems I used "FullSimplify" and "TrigReduce" but I manage to reduce more ...
1
vote
1answer
226 views
1
vote
1answer
174 views

Fitting data using a series of Sin and Cos

I have the following data representing the normal displacement caused by a normal load applied at the middle cross section of a cylinder: I've made the data available here. I am trying to fit ...
1
vote
1answer
610 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 ...
1
vote
1answer
396 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
vote
1answer
81 views

Inverse Laplace transform only returning exponentials

The inverse Laplace transform is only returning exponentials. I know it is from the definition $$ \frac{1}{2\pi i}\int_{\gamma - i\infty}^{\gamma + i\infty}F(s)e^{st}ds = \sum\text{Res} $$ However, I ...
1
vote
1answer
100 views

Conversion of Sine to Cosine

I'm solving equations with many Cosines and Sines. And I want to convert all the Sines to Cosines using trigonometric formulas such as cos(x)=sin(x+pi/2). How can I do this?
1
vote
1answer
138 views

Is there an inverse function for F[x] = {Cos[x], Sin[x]} in Mathematica?

Mathematica has functions ArcCos, ArcSin, and ArcTan, but none of these does what I need, ...
1
vote
1answer
83 views

How to apply a trigonometric identity to a formula

The product of cosines is given by (Wikipedia): $ \prod_{k=1}^{n} \cos{\theta_k} = \frac{1}{2^n}\sum_{e\in S} \cos(e_1\theta_1+\ldots+e_n\theta_n) $ where $S={1,-1}^n$. How can I apply this to a ...
1
vote
1answer
324 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 ...
0
votes
2answers
162 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
1answer
408 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

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
312 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 ...
0
votes
2answers
61 views

Binding trigonometric terms

I have many terms like A = Cos[Pi/18 + 2 x] + Cos[Pi/18 - 2 x] and I want to convert A to ...
0
votes
2answers
151 views

Expand 2f[x] to f[x]+f[x] (Simplify sums of ArcTan)

I'm trying to simplify an expression with sums of ArcTan, for which I've written a transformation rule that works for simple sums, so that ...
0
votes
2answers
114 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?
0
votes
2answers
305 views

How to insert trigonometric functions into matrices' vector components? [closed]

Is it possible to insert a trigonometric function into a matrix which will be able to be used dynamically, as an element of one of the vectors of the matrix? I'm trying to perform an operation like ...
0
votes
2answers
574 views

Simplifying a trigonometric equation to obtain specific terms

When I try to solve the non-homogeneous differential equation ...
0
votes
1answer
50 views

Why won't equal trig expressions simplify to the same form? [closed]

Trying to get Mathematica to do trig always stresses the hell out of me ... Why. won't. it. do. things?!? Why does ...
0
votes
1answer
87 views

Using conditional expressions

I did: Solve[Cos[x] == 1/2, x] And got: ...
0
votes
2answers
234 views

Simplify trigonometric equation knowing that $\sin(a)=n \sin(b)$

I was working on a problem involving trigonometry. I used Mathematica to help me in solving it. I ended up with this formula: ...
0
votes
1answer
119 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
2answers
62 views

How can I put the results of TrigFactor function into a more convenient form?

a1 D11 Cos[n x] + a0 a1 D11 Cos[n x] + 1/2 a1 a3 D11 Cos[n x] + 1/2 a2 a4 D11 Cos[n x] I have a large trigonometric expression. Can I factor out different ...
0
votes
2answers
56 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 ...
0
votes
1answer
160 views

Solving a Trigonometric parameter

I have a similar case as given before : Solving a Trigonometric function with one parameter Let: m = 1; Dx = 100; ν = 0.25; b = 1; and, ...
0
votes
1answer
68 views

strange result with trigonometric triple integral [duplicate]

I'm defining functions e[k_, t_] := Cos[Pi (k - 1) t] cosIntRaw[k_, l_, m_] := Integrate[e[k, t] e[l, t] e[m, t], {t, 0, 1}] cosInt[k_, l_, m_] := Assuming[Element[{k, l, m}, ...
0
votes
1answer
122 views

Mathematica can't simplify ellipse-related trig equation over reals?

f[t_] = -4 + Sqrt[(-Sqrt[3] + 2*Cos[t])^2 + Sin[t]^2] + Sqrt[(Sqrt[3] + 2*Cos[t])^2 + Sin[t]^2] The function above is identically 0 for all real values of t. ...
0
votes
0answers
77 views

Simplifying trig function

I'm trying to simplify a long expression of trig function. I'm not particularly good at trig identities or Mathematica, so this is turning out to be quite a task :( I tried Simplify, FullSimplify, ...
0
votes
1answer
60 views

Display trigonometry without Csc and Cot [duplicate]

I have a result with trigonometry functions using Cot and Csc. I would like to keep only cos, sin and tan and so prefer fractions in the display of the results. How is it possible to ask Mathematica ...
0
votes
0answers
57 views

Simplification of (Co)sine of a sum

I have a huge expression with (Co)Sine of a sum like Cos[[Theta] - 2 [Phi]] (after using \Simplify). I wanted to know if it exists a function which forces Mathematica to express the result in terms of ...
0
votes
1answer
85 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 ...