Questions tagged [trigonometry]

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

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Solving multivariable trig Identities

I'm trying to solve for a certain set of trig identities in terms of other trig identities. I saw this and this, but in my example, I have two tries: ...
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2 votes
1 answer
74 views

Reduce yields ArcTan instead of Pi/4

I expect this call: Reduce[Sin[x] - Cos[x] == 0, x, Reals] to return $x = \pi/4 + 2k\pi \ \vee \ x = -3/4 \ \pi + 2k\pi$. However, $\pi/4$ and $3/4\ \pi$ get ...
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5 votes
2 answers
254 views

How to pose simultaneous trigonometric equations problem in a way solvable by mathematica

Context: A camera at O has an image of a rectangular object ABCD. From the 2D coordinates of the image + the projection matrix of the camera I can calculate the direction vectors $\hat {A}, \hat{B}, \...
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  • 103
0 votes
0 answers
86 views

Simplification of long trigonometric expression taking a long time

I have tried to Simplify as well as FullSimplify a long trigonometric expression to get a simplified form of the expression but it takes a very long time almost hours and sometimes it also shows error ...
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2 votes
1 answer
78 views

How to do some trigonometric derivations

Two substitutions fail, so do I forget some earlier steps? For Cos[x] == Sin[(1/2)*Pi + x] /. x -> (1/2)*x = true I don't get the final answer, but only true. <...
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  • 649
9 votes
6 answers
590 views

Finding which given functions are equal to each others

I have about 50 piece functions (generally trigonometric functions). I want to find out which ones are equal to each other after some simplifications such as ...
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  • 483
4 votes
2 answers
92 views

Solving a set of trig inequalities

I have a set of inequalities Cos[a]Cos[b]>=Cos[t-a]Cos[b]&&Cos[a]Cos[b]>=Cos[t/2]&&Cos[a]Cos[b]>=Sin[t/2]&&a<=t<=Pi How to ...
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  • 270
4 votes
1 answer
119 views

Mathematica vs Rubi --- integrate $f(x,y) = x \sin^2 x + a x y$ --- Mathematica got this round? [closed]

Consider the function: $$ \begin{equation} f(x,y) = x \sin^2 x + a x y \end{equation} $$ with $a$ being a constant. We want to do the indefinite integral over $x$ and then over $y$. We do that using <...
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  • 4,113
1 vote
0 answers
18 views

How to sort out only terms that relates to certain variable in the results of TrigReduce? [closed]

I have a large function $F(\theta,\alpha_1,\alpha_2,...)$ which involves only trigonometric polynomial of these angles. I want to calculate $\frac{1}{2\pi}\int_0^{2\pi} Fd\theta$, but the function is ...
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2 votes
1 answer
91 views

Strange effect in the SphericalPlot3D [closed]

I found something odd in Mathematica when using the SphericalPlot3D command. Ranges for $x,y∈[0,2 \pi]$ are the same. All I do is swap sine and cosine. But when I ...
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1 vote
1 answer
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How can I get mathematica to prove $\sum_{k=0}^{n-1}\tan\left(\theta+\frac{k\pi}{n}\right)=−n\cot\left(\frac{n\pi}{2}+n\theta\right)$?

How can I get Mathematica to prove $\sum_{k=0}^{n-1}\tan\left(\theta+\frac{k\pi}{n}\right)=−n\cot\left(\frac{n\pi}{2}+n\theta\right)$ (1)? ...
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  • 325
0 votes
1 answer
40 views

Updating the association with answers from the TrigProperties Function

I have created a list of rules I would like to update with values. My goal here is to be able to write the following: ...
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0 votes
1 answer
55 views

NIntegrate giving different results after a change of variables

When I compute numerically the following double integral: \begin{equation} f(x,y)=\int_{-\infty}^{+\infty}da\int_{-\infty}^{+\infty}db\, \cosh\left[\frac{\sinh^{-1}(a)-\sinh^{-1}(b)}{2}\right]\, \exp\...
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  • 135
2 votes
1 answer
84 views

Calculate ArcTan in AceGen

I am working on a material model SMSStandardModule["Tangent and residual"] in AceGen and want to use command ToSphericalCoordinates for but AceGen is ...
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0 votes
1 answer
90 views

Solving a system of coupled trigonometric equations to find angles

I have a system of 9 coupled trigonometric equations (a 3X3 Matrix). I am trying to find four unknown angles $\theta_1, \theta_2, \phi_1, \phi_2$ by solving any 4 out of 9 such equations. $\text{M}=\...
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3 votes
2 answers
174 views

How to get the result of TrigFactor in terms of Cos

If I use TrigFactor, it gives the result in terms of Sin: In[483]:= expr := Cos[x] + Sin[x] TrigFactor[expr] Out[485]=Sqrt[2]*Sin[Pi/4 + x] What I want to get is <...
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3 votes
1 answer
217 views

Why can I not numerically integrate a smooth, integrable function?

Consider the function $\csc(t)\sin(3t)$ on the interval $[0,\pi]$. This is a perfectly well-behaved smooth function, as can be seen when plotting it: ...
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  • 755
3 votes
2 answers
144 views

Any way to get Mathematica to Solve[Sin[Tan[x]]-Tan[Sin[x]]==0,x]?

Solve[Sin[Tan[x]] - Tan[Sin[x]] == 0, x] It says it runs out of methods. After a very long time. Plotting the expression shows there are periodic solutions and ...
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3 votes
1 answer
181 views

Why reduce does not give solution for ArcTan[Tan[x]] == x?

Basic question I can't see why now. This works Simplify[ArcTan[Tan[x]] == x, Assumptions -> -Pi/2 < x < Pi/2] (*True*) But ...
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  • 108k
8 votes
3 answers
2k views

Why doesn't Mathematica know the exact value of some trivial trigonometric functions?

The trigonometric functions for half angles have well-defined and simple rules. For example $$\tan\left(\frac x2\right)=\frac{\sin x}{1+\cos x}=\frac1{\csc x+\cot x}$$ But I can't get the exact value ...
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  • 789
0 votes
0 answers
75 views

Maximize algebraic trigonometric function

I'm trying to maximize an algebraic function containing trigonometric functions: $$\mathrm{sol}=\frac{\sin\theta \cos(\alpha +\beta)\cos(\theta+\alpha+\phi)\cos\bar{\delta}}{\cos^2\alpha\cos(\alpha+\...
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  • 173
2 votes
1 answer
195 views

DSolve fails to find solution based on elementary function

I have two differential equations for which DSolve does not find a solution, however, there are simple solutions in terms of elementary functions, and more ...
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  • 4,113
2 votes
3 answers
153 views

Solving implicitly a trigonometric equation

I am trying to solve this equation with respect to L: L== ((9.81*T^2)/(2*Pi)) Tan[2Pi*d/L] Since you have the unknown ...
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1 vote
1 answer
52 views

Prevent automatic simplification of trigonometric functions with complex argument

I would like to prevent automatic simplification of some trigonometric functions involving complex numbers. The option AutosimplifyTrigs does the trick with 1/Cos[z], but not with Cos[I z]. ...
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6 votes
2 answers
792 views

Why does Mathematica not give the simple solution of the given equations?

I want to solve this system of two equations for $x$ $$\{ \sin (2\pi x)+\sin (\frac{2\pi}y)=0 \quad , \quad \cos (2\pi x)-\cos (\frac{2\pi}y)=0 \} \qquad (1)$$ I use ...
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  • 119
0 votes
1 answer
79 views

Plotting equation with some unknown parameters

I am new to the Mathematica and I have a question about the plotting. I am trying to plot the transcendental equation $$\tan{(z)}=\sqrt{\frac{1}{2m_0}\left (\frac{z_0}{z}\right)^2-1} $$ where the ...
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0 votes
1 answer
66 views

How to solve for when this trigonometric function intersects the line $y=1$?

How can I solve for $\alpha$ in $$4\sin\left(\frac{\alpha}{2}\right)\cos\left(\frac{\alpha}{2}\right)^{3}\left(t-r\right)+\sin\left(\frac{\alpha}{2}\right)=1$$ on the domain $0\leq\alpha\leq\pi$? ...
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7 votes
2 answers
138 views

Why does FunctionPeriod give two different results for alternative forms of the given function?

I have a function for the variable $x>0$ and constant $a\in\mathbb{R}$. I write it in its two alternative forms $$f(x)=\cos a\pi-\cos x\pi =-2\sin\frac{(a-x)\pi}{2}\sin\frac{(a+x)\pi}{2} $$ Then, I ...
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  • 335
1 vote
0 answers
78 views

Is there a function in Mathematica to combine/decompose sinusoids? [closed]

Lets say I have some combination of an arbitrary number of sinusoids with potentially varying magnitudes, phase angles and frequencies that I would like to compose into a singular sinusoid, is there a ...
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-1 votes
1 answer
105 views

Solve A System of Trigonometric Equations

I tried running the following code on Mathematica Cloud, but it didn't because it was taking long of I have the basic plan. Would someone please run this code for me and share with me the results. it'...
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3 votes
1 answer
136 views

Simplifying a difficult trigonometric sum

As this video shows, $$\tan \left( \frac{3 \pi}{11} \right) + 4 \sin \left( \frac{2 \pi}{11} \right) = \sqrt{11} .$$ The direct and obvious methods for Mathematica to find this solution do not work: <...
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0 votes
1 answer
107 views

How to simplify complex Trigonometric expression in mathematica? [closed]

The expression which I need to simplify in mathematica into simplest form ...
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2 votes
0 answers
134 views

Does Mathematica know about trig identities?

I am calculating some geometry via two different ways in Mathematica. One uses a known trig identity the other doesn't. We define angles of two right-angle triangles. ...
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2 votes
2 answers
61 views

Removing transient part in equation and solving for a general form

I have the following code that I run: ...
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  • 1,723
2 votes
1 answer
101 views

NIntegrate fails to solve a double oscillatory integral

I need to compute the following integral: ...
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  • 135
0 votes
1 answer
62 views

How solve this system of trigonometric equations?

I have the following system of equations: (substituting any real values for a,b,c,r,Alpha,Beta will return the same answer for x) ...
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  • 103
2 votes
1 answer
143 views

Returning trigonometric value answers in irrational form

I need to find the irrational form of Sin[7*\[Pi]/8]. But in Mathematica, I can get its numerical value. I am getting ...
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  • 1,163
1 vote
1 answer
52 views

Why if I change the function Sine to discrete Sine the plot is difference

I would like to know why when I change +1 in a discrete Sine change the list line plot and when I plot the function sine anything change. ...
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1 vote
0 answers
47 views

How can I prevent Mathematica to simplify basic trigonometric identities (1/Cot(x))? [duplicate]

I'm working on a code to display(Print[]) the answers of some excercises for my students. Some of the answers have parts like 1/Cot(x). I want to prevent Mathematica to transform this expression into ...
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4 votes
1 answer
139 views

Determining Mean Path Length

I'm interested in working out the average path length in a square. Assume at a single point within the square, photons are released in every direction. I'm interested in determining the average path ...
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  • 3,842
0 votes
3 answers
55 views

How to fix a reduce function error when using trigonometric functions?

For example, if I'm trying to find out when the function is greater than or equal to 20 it gives an error. I also trying defining my trig equation as a function and tried to solve that (e.g Reduce[h[t]...
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  • 137
2 votes
1 answer
217 views

Is it possible to ask Mathematica to give a table of probability that $f(x)>0$?

I have a function $$f(x)=(4 \cos 2 a x+3) (\cos a x+2 \cos 300 x),$$ and I want to calculate the probability that $f(x)>0$ for $a=\{1,2,3,...,100\}$ assuming that $x$ has uniform distribution. More ...
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  • 1,069
7 votes
1 answer
348 views

CORDIC - Volder's algorithm

As the title suggests, the object of this topic is the CORDIC algorithm (COordinate Rotation DIgital Computer). Although it's now obsolete in most cases, I think it can be interesting to understand ...
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  • 4,281
1 vote
1 answer
91 views

How to extract angle $0 \le \varphi < 2 \pi$ from a complex number $a + i \, b$?

Suppose you have a complex number of the standard shape $z = a + i \, b$ (where $a$ and $b$ are real numbers). How can we convert it to the polar shape $z = A \, e^{i \varphi}$? More specifically, I ...
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  • 3,533
0 votes
1 answer
109 views

Building complex signals in Mathematica

How to build a particular signal in Mathematica such that we have a sine curve for half cycle, then have zeros for some time and this continues? It is simple to have the zeros for the second half ...
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3 votes
2 answers
186 views

Applying the identity $\sin^2 + \cos^2=1$ without any other trigonometric simplifications [closed]

Mathematica does not automatically simplify $\sin^2 + \cos^2 =1$, but applying any kind of trigonometric simplification results in not only that identity being applied but also all kind of trig ...
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1 vote
1 answer
47 views

How can I understand the 2nd solution of this equation? (theoretically correct, but doesn't work while being verified)

I'm trying to solve these two equations: $$ \cos\left(\frac{\gamma'}{2}\right) = g_0\qquad e^{i\beta'}\sin\left(\frac{\gamma'}{2}\right) = g_1 $$ Where $g_0$ is real and $g_1$ is complex. From the ...
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  • 115
0 votes
1 answer
64 views

How can I substitute values into this set of equations?

I'm new to Mathematica and I'm trying to solve this set of trig equations (I'm not exactly sure if the syntax looks correct): ...
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  • 115
11 votes
0 answers
254 views

Series with ArcTan gives wrong symbolic answer in Wolfram Language

Bug introduced after 9 and persisting through 13.0 Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression! When calculating ...
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  • 211
2 votes
3 answers
114 views

How to solve this inequality correctly?

Find the value range of real number a, so that for any real number x and $\theta \in\left[0, \frac{\pi}{2}\right]$, make $(x+3+2 \sin \theta \cos \theta)^{2}+(x+a \sin \theta+a \cos \theta)^{2} \...
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