Questions tagged [trigonometry]

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

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2
votes
1answer
201 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 ...
5
votes
0answers
138 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 ...
0
votes
1answer
70 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
votes
2answers
142 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 ...
1
vote
1answer
39 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 ...
0
votes
1answer
49 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): ...
2
votes
3answers
104 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} \...
1
vote
1answer
56 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? ...
-5
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1answer
81 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.
3
votes
2answers
190 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 ...
1
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0answers
70 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 ...
0
votes
2answers
96 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] ...
0
votes
1answer
52 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 ...
0
votes
1answer
70 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 ...
1
vote
1answer
29 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: ...
1
vote
1answer
69 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
votes
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
votes
2answers
93 views

Levin Rule Integrate Power of Oscillating Function

I want to numerically integrate a function of the form: ...
5
votes
4answers
314 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
votes
2answers
196 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 ...
0
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2answers
73 views

Simplifying expression involving Trignometric functions

Mathematica is not simplifying the following function. I have tried TrigExpand, FullSimplify, etc. Nothing is working. ...
1
vote
0answers
131 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
votes
0answers
51 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
votes
1answer
71 views

How to prevent TrigReduce auto evaluating Sin and Cos

Mathematica automatically evaluates Sin and Cos when TrigReduce is applied. For example, <...
1
vote
1answer
71 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
votes
1answer
132 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
votes
1answer
48 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 ...
1
vote
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 ...
0
votes
1answer
83 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
votes
1answer
80 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
votes
1answer
106 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
votes
1answer
188 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
votes
1answer
42 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 ...
9
votes
3answers
452 views

Why is the solution I obtained from Solve not verified in the original equation?

I have this equation $$x^2 \left(\sqrt{1-y^2} \sin (x)-\sin (4 x)\right)+2 x y=0$$ I want to solve this equation and find $y$ in terms of $x$. I use Solve ...
0
votes
0answers
87 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 ...
2
votes
1answer
87 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: ...
0
votes
2answers
73 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] ...
0
votes
0answers
28 views

Why does Mathematica shade a region when this code is inputted? [duplicate]

Cos of 2Pi is plotted differently than Cos of 1000Pi, that doesn't make sense being their equivalent. See the region in the picture.
1
vote
3answers
117 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. ...
1
vote
2answers
129 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: ...
2
votes
1answer
39 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]]}}]
3
votes
1answer
74 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, ...
0
votes
1answer
47 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 ...
0
votes
0answers
38 views

Problem with solve : from trigonometry to polynomials

I want to solve a trogonometric problem by transforming it to polynomial : ...
0
votes
1answer
67 views

Calculate the volume of objects in Graphics3D

Is there a way to calculate the volume of these different regions without making the algebra ? ...
2
votes
0answers
55 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 ...
1
vote
0answers
86 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 ...
1
vote
3answers
92 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, ...
1
vote
1answer
51 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 ...
0
votes
0answers
57 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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