# Questions tagged [trigonometry]

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

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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 ...
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 ...
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 $0\leq\alpha\leq\pi$? ...
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 ...
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 ...
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'...
92 views

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

The expression which I need to simplify in mathematica into simplest form ...
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. ...
56 views

### Removing transient part in equation and solving for a general form

I have the following code that I run: ...
98 views

### NIntegrate fails to solve a double oscillatory integral

I need to compute the following integral: ...
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) ...
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 ...
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. ...
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 ...
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 ...
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]...
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 ...
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 ...
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 ...
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 ...
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 ...
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): ...
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 ...
108 views

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 ...
124 views

### Levin Rule Integrate Power of Oscillating Function

I want to numerically integrate a function of the form: ...
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 ...
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 ...
74 views

### Simplifying expression involving Trignometric functions

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

### How to prevent TrigReduce auto evaluating Sin and Cos

Mathematica automatically evaluates Sin and Cos when TrigReduce is applied. For example, <...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $y(x)$ ...