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

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1answer
69 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 ...
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1answer
117 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 ...
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1answer
300 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 ...
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1answer
225 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 ...
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2answers
171 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 ...
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1answer
274 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 ...
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2answers
112 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 ...
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2answers
87 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?
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2answers
140 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 ...
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2answers
443 views

Simplifying a trigonometric equation to obtain specific terms

When I try to solve the non-homogeneous differential equation ...
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1answer
112 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 ...
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1answer
52 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}, ...
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1answer
108 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. ...
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0answers
59 views

Why does Mathematica have trouble with this simple set of simultaneous equations? [on hold]

The code in question is: Solve[{x == r*Cos[\[Theta]], y == r*Sin[\[Theta]]}, {r, \[Theta]}]. I'm a newbie so this might be fairly basic, but shouldn't this work? ...
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1answer
96 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, ...
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0answers
30 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 ...
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0answers
14 views

Prevent trigonometric simplification [duplicate]

I have created a plot of g(x)=a*sin(b(x-c))+b where a, b, c, and d change using sliders excetera. Also, the trig function itself func = (sin, cos, tan) is selected using buttons. My issue is with the ...
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1answer
181 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. ...
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0answers
69 views

Algebraic condition from a non linear equation

I have got a system of equations which look like this: $\theta_{1}^{2}e^{\phi_{1}\cos(\Omega z)}\tilde{w}\cos^{2}(\theta_{1}\sin\Omega z)\sin^{2}\Omega z+\frac{1-\lambda\cos(2\theta_{1}\sin\Omega ...
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1answer
66 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 ...
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0answers
59 views

Trying to solve a trig identity [migrated]

Given $\sin 2x+\sin x=1$, find the value of $\cos 2x+\cos 4x$. I know $\cos 2x+\cos 4x \implies 1-2\sin^2x+1-2\sin^22x$, but didn't get the answer.