Questions tagged [trigonometry]

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

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0answers
43 views

How do you symbolically expand a trigonometric expression? [closed]

Suppose I want to prove Sin[2x] - Cos[2x] and 2 Cos[x]Sin[x] + (Sin^2)[x] - (Cos^2)[x] are the same value symbolically how do i ...
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1answer
65 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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1answer
63 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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2answers
136 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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0answers
72 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 ...
-1
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1answer
95 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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1answer
92 views

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

The expression which I need to simplify in mathematica into simplest form ...
2
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0answers
132 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. ...
2
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2answers
56 views

Removing transient part in equation and solving for a general form

I have the following code that I run: ...
2
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1answer
98 views

NIntegrate fails to solve a double oscillatory integral

I need to compute the following integral: ...
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1answer
53 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) ...
2
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1answer
137 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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1answer
50 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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0answers
45 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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1answer
130 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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3answers
52 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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1answer
211 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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0answers
167 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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1answer
105 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 ...
3
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2answers
149 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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1answer
41 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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1answer
56 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): ...
10
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0answers
198 views

Series with ArcTan gives wrong symbolic answer in Wolfram Language

Bug introduced after 9 and persisting through 12.3.1 Recently, I have found a very bad problem with Wolfram Language. It gives the wrong answer for a quite simple expression! When calculating ...
2
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3answers
108 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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1answer
60 views

How to remove "higher/lower harmonics" from expression

let's say we are given $\sum_{k=0}^n a_k \cos(k \omega t)$. How can we tell Mathematica to neglect all terms in the above expression for which $k_1>k > k_0$, where $k_0$ and $k_1$ are specified? ...
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1answer
85 views

How would you use mathematica commands to produce this? image of problem provided

I'm just starting to use mathematica so seeing how this problem is done will help me a lot. Thank you.
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2answers
198 views

Two values of ArcCos not showing

When I try to find θ = ArcCos[-.5] I am expecting more than one answer: $$2 \pi/3, 4\pi/3,...$$ But Mathematica is returning only one: 2.0944 and it is not in ...
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0answers
72 views

How to get a result for $\int{\sqrt{a^2 \left(\sin{a x}-2 \sin{2 a x}\right)^2+1} \, \mathrm{d}x}$?

I want to obtain the result of this integral where $\mathbb{R}\ni a,x>0$ $$\int{\sqrt{a^2 \left(\sin{a x}-2 \sin{2 a x}\right)^2+1} \, \mathrm{d}x}$$ but Mathematica does not give an answer. Of ...
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2answers
100 views

How to extend this integration to all the reals?

Doing an exercise on calculus with 12.2 on Windows 10 Pro, I obtain a = Integrate[Sqrt[1 + Sin[t]], {t, 0, x}, Assumptions -> x \[Element] Reals] ...
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1answer
63 views

Derivatives of trigonometric functions

Let's use the following sample case Clear["Global`*"]; t1 = ArcTan[y/(x - x1)]; f = (3*(Cos[t1])^2 - 1); der = D[f, x] which gives ...
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1answer
72 views

Does anyone here know how can we extract Lambda from the following equation

I am working on an estimation problem where I have the following Code is A = 1 + Pi*Csc[(1 + Pi)*\[Lambda]]^2* (Pi + Sin[2*(1 + Pi)*\[Lambda]]) Can anyone ...
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1answer
31 views

How to make a long sum of trigonometric functions into an list of those individual functions?

I have a few long sums over many trigonometric functions. One of these is shown below. I would like to place each of the individual components into a list of functions. Like: ...
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1answer
73 views

Symbolic Integration with trigonometric functions

I have this trigonometric integral which takes forever to evaluate $\int dx \frac{4 \left(\cos \left(p_1 x\right)-\frac{\sin \left(p_1 x\right)}{p_1 x}\right) \left(\cos \left(p_2 x\right)-\frac{\...
4
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3answers
1k views

How to make mathematica give 1/0 as infinity

I would like Mathematica to print $\arctan(4/0)$ as $\frac{\pi}{2}$ but it does not because in mathematica 1/0 is complexinfinity. How do I make it print n/0 as Infinity so that Arctan will give me ...
3
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2answers
124 views

Levin Rule Integrate Power of Oscillating Function

I want to numerically integrate a function of the form: ...
5
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4answers
324 views

NIntegrate Oscillating kernel

I have a finite highly oscillating integral of the type: NIntegrate[x^2 Exp[I f[x] s] , {x, 0, 1}] where f is a simple function ...
5
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2answers
219 views

Solving trigonometric equations with two variables in fixed range?

I am trying to use 'Solve' function to solve two trigonometric equations with two variables a1 and a2 (with range ...
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2answers
74 views

Simplifying expression involving Trignometric functions

Mathematica is not simplifying the following function. I have tried TrigExpand, FullSimplify, etc. Nothing is working. ...
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0answers
137 views

Simplify trigonometric functions to take the Laplace transform

I have one trigonometric function which is simplified as f[t_, RV_, H_] := 0.000308148 H Cos[0.172439 RV Sin[2 \[Pi] t]] It is an input to one ODE which I want to ...
2
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0answers
58 views

Trigonometric Simplification and Double Angle Formula

I am trying to achieve the formula hbar / 2 * cos(wt) * sin(theta). However, my Mathematica expression doesn't seem to simplify the half/double angle formulas. I am ...
2
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1answer
76 views

How to prevent TrigReduce auto evaluating Sin and Cos

Mathematica automatically evaluates Sin and Cos when TrigReduce is applied. For example, <...
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1answer
78 views

How to convert trigonometric values to AlgebraicNumber

It is known that trigonometric functions evaluated at rational numbers of degrees are algebraic, and Mathematica recognize this: for example ...
4
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1answer
145 views

Solving a trigonometric equation with discrete solutions

So I know that trigonometric equations show up here very often, but this one is particularly difficult and important to me, so that I was hoping to get some valuable hints from people who know more ...
0
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1answer
49 views

$\alpha \int_{0}^T \text{Sin}(fi−fk+Δf)∗t) \, dt$ — Why is it not giving wrong answer? [closed]

$$\alpha \int_{0}^T \text{Sin}(fi−fk+Δf)∗t) \, dt $$ I am integrating this in Mathematica, My code is (1/2)*α*Integrate[Sin[2*Pi*(fi - fk + δf)*t], {t, 0, T}] + Ν1 ...
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1answer
43 views

Trigonometric question combined with questions about Mathematica

I'm new to Mathematica and I am struggling with the Syntax and the functions of this "programming" language. I'm looking for a way to solve sin2 α cos3 α = tan4 α But if I try to run it ...
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1answer
88 views

Simple Question: How to simplify what is inside the Sin function like below?

I have this code of Mathematica (1/(2 (fj - fk) π)) Cos[(fj - fk) π T + (fj - fk) π (T + δt)] Sin[(fj - fk) π T - (fj - fk) π (T + δt)] There are a few ...
3
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1answer
84 views

Establish the equivalence of two inverse trigonometric function based formulas

In a comment to 3D5D user JimB provided an answer to the question posed there of finding the "two-quater[nionic]bit" absolute separability Hilbert-Schmidt probability. (Previously, in ...
3
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1answer
109 views

Expressing functional dependency given trigonometric relations

Given (assuming $0 \leq t \leq \pi/2$) x == (1 + a Sin[2 t]) Sin[t], and y == 1 - (1 + a Sin[2 t]) Cos[t] How can I get $y(x)$ ...
2
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1answer
211 views

How to symbolically solve this transcendental equation

The equation below shows up when dealing with geodesic curves on elliptic paraboloids: \begin{equation} u-c^2=u(1+4c^2)\sin^2\left(v-2c \ln\left(k(2\sqrt{u-c^2}+\sqrt{4u+1})\right)\right) \tag{1} \...
0
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1answer
52 views

Signed vector angle over an array

I am calculating signed vector angles (limited to {-Pi,Pi}), but the twist is that these calculations are being done in the context of a 'landscape' array. I have a point on a 2D landscape and a ...

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