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

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1
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3answers
156 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 ...
0
votes
0answers
25 views

Point Calculation Mystery - Mirror axis at 45º? [closed]

I've calculated a point in my map view using the users position, the bearing, and the distance to that point with the help of that post: ...
2
votes
1answer
44 views

Simplify trigonometric expression

Mathematica correctly simplifies the following expression: ...
1
vote
1answer
37 views

find the inverse of a hyperbolic function

Hi everyone I am new in Mathematica and I am trying to find the inverse of a function which contains hyperbolic tangents and I hope someone can help me. The function is y=(a)tanh(d(x-g))+ ...
0
votes
2answers
91 views

Find *all* numerical solutions to cosine based equality

To help with http://astronomy.stackexchange.com/questions/11456/ I'm trying to find all numerical solutions to: 5.20427*Sin[0.529699*t] == Sin[2*Pi*t] Since the period of the first function is ...
4
votes
3answers
162 views

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 ...
0
votes
1answer
30 views

Expanding a function with trigonometric expressions in a controlled manner by excluding addition identities

I want to simplify a nonlinear equation with trigonometric terms. After I've expanded I don't want to loose open terms to Trigonometric Addition Formulas ...
6
votes
1answer
103 views

Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...
1
vote
1answer
65 views

How to reduce trigonometric expressions under special conditions

For the following problems I used "FullSimplify" and "TrigReduce" but I manage to reduce more by hand. ...
5
votes
2answers
168 views

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 ...
0
votes
2answers
69 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
1answer
55 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
0answers
101 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, ...
4
votes
1answer
93 views

Transforming expressions in terms of Csc and Sec to expressions in terms of Sin and Cos [duplicate]

I am writing a code to compute some matrix quantities. The result involves Sec andCsc functions, and I want a form displayng ...
1
vote
2answers
74 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]] ...
0
votes
1answer
76 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 ...
2
votes
2answers
221 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 ...
6
votes
2answers
268 views

Evaluating complicated trig without resorting to numerical methods

I have an angle theta given by Kx = (2/Sqrt[3]) ArcSin[Sqrt[3/10]]; Ky = (2/3) (ArcCos[(1/5) Sqrt[7/10]] - Pi); theta = Cos[ArcTan[Kx, Ky]]; This evaluates, by ...
0
votes
1answer
112 views

Using conditional expressions

I did: Solve[Cos[x] == 1/2, x] And got: ...
3
votes
3answers
301 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 ...
2
votes
2answers
144 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 ...
3
votes
0answers
111 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 ...
1
vote
1answer
88 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 ...
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 ...
1
vote
1answer
131 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?
0
votes
2answers
252 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: ...
1
vote
1answer
170 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, ...
2
votes
0answers
82 views

TrigExpand Idiosyncracies

TrigExpand[Sin[x]^2 Log[y]] returns sin^2(x) log(y), as one would expect. However, ...
1
vote
2answers
70 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 ...
6
votes
2answers
247 views

Apply Trig Identity to Transform Sum of Sinusoids into Phase-Shifted Cosine Function

I'm trying to solve for the output of a simple RC low-pass filter, with Cos[w t] input. The convolution of the input with the RC transfer function gives me the right output, but I'd like to be able to ...
0
votes
2answers
183 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 ...
10
votes
1answer
313 views

Mathematica 10 unable to Simplify[Cos[2 ArcCos[A]]]

Mathematica 10 evaluates Simplify[Cos[2 ArcCos[A]]] as Cos[2 ArcCos[A]], instead of the desired ...
4
votes
1answer
282 views

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: ...
3
votes
1answer
359 views

Mathematica takes too long to solve this

I have the following system of equations: ...
1
vote
1answer
89 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 ...
0
votes
1answer
161 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, ...
4
votes
1answer
197 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]]]]] ...
13
votes
5answers
941 views

Solve symbolically a transcendental trigonometric equation and plot its solutions

I currently have the equation below for a beam with a hinge at various locations, the variable a can vary between 0 and 0.5. $$ Tan\left( {a\sqrt \alpha } \right) + Tan\left\{ {\left( {1 - a} ...
0
votes
2answers
166 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
0answers
67 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 ...
20
votes
1answer
525 views

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 ...
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
2answers
128 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?
2
votes
2answers
400 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
642 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. ...
10
votes
3answers
1k views

Simplifying trig expressions containing Sqrt or Abs

The following Maple code can simplify abs(sin(x)) into -sin(x) given the condition ...
3
votes
2answers
160 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 ...
1
vote
1answer
266 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 ...
2
votes
1answer
267 views