Questions tagged [trigonometry]

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

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95 views

Symbolic solution of differential equation with trigonometric initial conditions

We observe that D[Tanh[x3[t]], t] == Sech[x3[t]]^2 Derivative[1][x3][t] and that ...
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1answer
92 views

Mathematica outputs a trigonometric integral ($\sec^3$) in a form I can't prove

The indefinite integral is of course $1/2 ( \sec(x) \tan(x) + \ln | \sec(x) + \tan(x) | ( + C)$. Mathematica gives: ...
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2answers
75 views

Solve can not solve the equation correctly in Reals

Here is the error I found. r = 3; Solve[Sqrt[(r^2 Cos[m Pi] - x)^2 + (r^2 Sin[m Pi])^2] == 10 && x > 0 && 0 <= m <= 2, x, Reals] ...
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137 views

Non linear model fit with trigonometric model

I tried to fit the curve of the dataset. I used 'Nonlinearmodelfit' function to get the specific fitted equation. Yes, I can get the result, but I am wondering there is a way to improve the result. ...
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2answers
178 views

FindFit with a Sin function

I'm trying to find the fit of Sin-shaped weather data that is provided by Wolfram. My code is as follows: ...
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1answer
41 views

Solving simple trig equation [closed]

I tried to solve a simple trig equation. Solve[{Sin[x] == Cos[x], 0 <= x <= Pi}]; The answer should be pi/4 But I get simplify[{{x -> -2 ArcTan[1 - Sqrt[2]]}}]
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1answer
79 views

Solve an equation with real parameters

I am trying to solve $$ \left(\eta ^2-1\right) \cosh ^2(\beta \eta )+2 J^2=2 \eta (J \sinh (\beta \eta ) \sinh (\beta J)+\eta \cosh (\beta \eta ) \cosh (\beta J)) $$ for $\eta$. Where, $\beta, ...
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1answer
48 views

Applying the command "expr/.rule", to find the expansion of Cos[a+b]

how can i find the expansion of Cos[a+b], using the expression g[f[{a,b}]].So i am specified to use one shot replacement to get the expansion by replacing the argument of the expression given. I tried ...
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39 views

Problem with solve : from trigonometry to polynomials

I want to solve a trogonometric problem by transforming it to polynomial : ...
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1answer
69 views

Calculate the volume of objects in Graphics3D

Is there a way to calculate the volume of these different regions without making the algebra ? ...
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0answers
57 views

Why Integrate does not obtain this conditional result automatically for orthogonality of cosines?

V 12.1 on windows. I remember asking something similar many years ago. I was hoping Mathematica now could have done this automatically: $$ \int_{-\pi}^{\pi} \cos (n x) \cos (m x) \, dx $$ For ...
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90 views

Help with double pendulum equations

I'm 16 and I'm pretty new to Mathematica. I've been working on a personal coding project which has some funky maths in it and I am kinda struggling. I've solved for the 4 polynomials but they answers ...
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3answers
109 views

Loosen tolerances to get a solution from NSolve for trig system

This is more an exercise in learning Mathematica than a real issue because the solution for me is just to solve half of the system. I have a simple system of trig equations and can't solve the angle, ...
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1answer
52 views

Solving trigonometric equations

I need to solve these three trigonometric equations, and figure out the a, b and c. But, this takes too long time, and I am not sure the answer is right. Thus, How can I progress my code to speed it ...
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59 views

Why can't Mathematica maximize simple trigonometric Expression?

Explain please why such simple function won't be accomplished. MaxValue[{a*Sin[x], a > 0}, x,Reals]. And how to solve this type tasks?
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3answers
109 views

Simplify Trigonometric Expressions so that they no longer contain specific Trigonometric Ratios [duplicate]

I want to simplify the following Trigonometric expression so that it no longer contains Tan[a] and Cot[a]. How can I do that? <...
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2answers
565 views

Can Mathematica solve A Sin[t]^2 + B Cos[t]^2==1 for {A,B}?

Can Mathematica solve A Sin[t]^2 + B Cos[t]^2==1 for {A,B}? The solution to the statement ...
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2answers
57 views

Having problem in solving hyperbolic functions

I am trying to solve Upm/Um at different points but I am not getting any result. There is any problem with my hyperbolic function? Please help me to get the results. It will be appreciated. ...
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1answer
136 views

Could anyone help me find the EXACT value?

Could anyone please help me find the EXACT value (not numerical value) of this by Mathematica or by mathematical reasoning? Thanks a lot. ...
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1answer
81 views

I am unable to solve angle of a trigonometric equation

I am fairly new to Mathematica, so this may be a simplistic question, but I want to learn. I know how to use the Solve function to solve a single equation like this: $$\cos[41.614-x]-1.2752|cos[1....
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3answers
243 views

Why doesn't Mathematica simplify $\cos^2(x)+\sin^2(x)$? [closed]

I'm new in mathematica, and there is a lot of things that I'm still missing... I have this expression: ...
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1answer
44 views

Finding local minima of this transcendental equation

I'm trying to find all the local minima of the following function, symbolically: ...
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1answer
104 views

Solving a system of trigonometric equations. with NSolve

Is numerical solving of the problem in the picture below even possible? Edit: The code does not output anything, it just runs for 20min+ ...
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1answer
227 views

Solve can't solve my trigonometric equation—why?

I have the following equation for epsilon $2 |\alpha_{n,ch}|=\epsilon+\cos^{-1}(\tan(\frac{\pi}{4}-\frac{\epsilon}{2}))$, where $\alpha_{n,ch}$ is a negative constant (e.g. -0.769) I tried to solve ...
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1answer
65 views

How do I apply complicated algebraic/trigonometric manipulations to nested expressions?

Consider the expression $$ a\sin(x)-a\sin\left(\frac{x}{a}\left(a+\frac{ay}{x}\right)\right) \label{a}\tag{1} $$ which can be rewritten as $$ \sin(x)-\sin\left(x+y\right) \label{b} \tag{2} $$ and ...
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4answers
428 views

Evaluate the defining Integral of the Bessel functions of the first kind

I am trying to evaluate the integrals $$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}(x\sin t - nt)} \mathrm{d}t $$ and $$ \int\limits_{-\pi}^{\pi} \mathrm{e}^{\mathrm{i}x\sin t} \mathrm{d}t $$ ...
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0answers
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How to get Trig Form from Root

Simplify`TrigToRoot[Cos[Pi/9]] gives out Root[-1 - 6 #1 + 8 #1^3 &, 3] But when I want to do the inverse operation: <...
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1answer
214 views

Atan2 function unwrap [closed]

I use atan2 function in my calculations. The results are as follows: Matlab has the unwrap function, and it copes well with the correction of such plots. How to do it in Mathematica?
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1answer
59 views

Cannot seem to find the syntax to evaluate a trig expression [closed]

3*Cos[t] == Cos[Sqrt[3]*t] between the values t=0 and t=1 Thanks for any help.
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2answers
139 views

Volume integration with a condition

I have a set of parameters $x_1, \dots x_4 \in (0,1)$. I want to find the volume of the subregion of this 4d cube satisfying $$\sin^{-1}(x_1)+ \dots +\sin^{-1}(x_4) > \frac{3\pi}{2}$$ I've tried ...
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2answers
93 views

How to simplify this sums of exponentials?

I got expressions that look like $$ \frac{1}{2} \mathrm e^{-\mathrm i r x} \left[\mathrm e^{2\mathrm i r x} \left(1 + \mathrm e^{-2\mathrm i x}\right)^r + \left(1 + \mathrm e^{2\mathrm i x}\right)^r\...
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2answers
88 views

Primitive of a continuous function over $\Bbb R$

A continuous function over $\Bbb R$ has a primitive that is also continuous over $\Bbb R$. However, it often happens with Mathematica and other CAS that the result is not continuous, especially with ...
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1answer
74 views

Why does the Euler identity not seem to be recognized in Mathematica? [closed]

Why does the following equation: E^(I*theta) === Cos[theta] + I*Sin[theta] yield false, in terms of Euler's Identity?
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2answers
83 views

Using Reduce to solve trig equations. Error: unable to decide whether numeric quantity .. is zero

I'm trying to find solutions to a fairly simple pair of simultaneous equations in variables $\phi_1, \phi_2$ using Reduce. ...
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1answer
283 views

How to use Mathematica to simplify this kind of trig sum?

$$ S=\sum_{k=0}^{10}\sin\left(\frac{(2+4k)\pi}{23}\right) =\sum_{k=0}^{10}e^\left(i\frac{(2+4k)\pi}{23}\right) =e^{i\frac{2\pi}{23}}\sum_{k=0}^{10}e^{i\frac{4k\pi}{23}} =e^{iu}\sum_{k=0}^{10}\left(e^{...
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0answers
48 views

How to find the minimum positive period of a function [duplicate]

Through Sin[x]^6 + Cos[x]^6 // TrigReduce operation, we can know that the minimum positive period of Sin[x]^6 + Cos[x]^6 is <...
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1answer
122 views

Does Mathematica know about identity involving ArcSin(Cos(x))? [duplicate]

Given that $0 < x < \pi/2$, it can be shown that $$\arcsin(\cos(x)) = \pi/2-x,$$ however, I was unable to make Mathematica to simplify the LHS into the RHS. I was guessing that, ...
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0answers
148 views

Reduce[Sin[x]==0,x] splitting odd and even multiples of Pi

as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem Reduce[Sin[x] == 0, x] for which I obtain the ...
4
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1answer
63 views

Trigonometric identity not simplifying

I have a pair of numbers {x,y} (Reals or Integers) for which I want to confirm symbolically that ArcTan[y/x]+ArcTan[x/y]==Pi/2 Here is my attempt: ...
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0answers
75 views

Elimination of trigonometric functions [closed]

I want to eliminate $\gamma$ from the system of equations given below: ...
7
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3answers
182 views

Finding points in a plane

The end of the Star Wars saga is near, so I feel compelled to design a Mouse Droid. Based upon the Paul Murphy's schematics I've reconstructed the outline of the top shell: Since my goal is to ...
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2answers
1k views

How to draw a phasor animation with Mathematica?

There is a nice animation on the Phasor Wikipedia page: I wonder if (and how) one could draw such animation with Mathematica? I'm not necessary interested in the code required to draw the exact same ...
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1answer
87 views

How can I solve this trigonometric equation system?

As the picture shows,there are four equations and three angles,\theta1,\theta2,\theta3. I need to solve the values of this three angles. If the range of the angles needed, then consider (-Pi,Pi). BTW, ...
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0answers
104 views

Minimal Surface of Revolution - Integrate Challenge

I'm trying to use Mathematica to go from equation (11) to equation (12) in this example of a Minimal Surface of Revolution. There is a MMA notebook on that link, but it only shows how to find the ...
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1answer
100 views

Simplify product of cosh and sech expressions

I would like to simplify a product of hyperbolic cosine and hyperbolic secant functions, with the key simplifying assumption being that the two are inverses of each other. This sounds like a silly ...
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1answer
47 views

Solving complex trig quations - missing solutions?

{ Sin[Pi/2 + I*Log[2 + Sqrt[3]]], Sin[Pi/2 - I*Log[2 + Sqrt[3]]], Sin[Pi/2 + I*Log[2 - Sqrt[3]]], Sin[Pi/2 - I*Log[2 - Sqrt[3]]] } // FullSimplify ...
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2answers
137 views

How to generate random waves

I want to generate a set of $N$ random waves, where the wave vector and phase are random numbers, this is my code ...
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2answers
184 views

Solar Power Calculations

Good Afternoon, I have calculated the Incident beam radiation for a given locations local sunlight hours. ...
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1answer
70 views

how to solve equations

I am trying to find the values of L and \theta, but mathematica is unable to produce output. My code is given below, where the value of k is fixed, i.e., 0.75, but the value of B can be positive or ...
9
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1answer
337 views

Why ArcTan[1, 0. I ] yields -1.5708+0. I?

Bug introduced in 5.2 or earlier and persisting through 12.0.0 Why ArcTan[1, 0. I ] yields -1.5708+0. I ? The result should ...

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