Questions tagged [trigonometry]

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

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3answers
89 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: ...
2
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1answer
37 views

Finding local minima of this transcendental equation

I'm trying to find all the local minima of the following function, symbolically: ...
1
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1answer
96 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+ ...
6
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1answer
167 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
60 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
212 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
20 views

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: <...
2
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1answer
72 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
43 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.
6
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2answers
117 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
79 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
77 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 ...
0
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1answer
49 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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0answers
57 views

Mollweide plot of Sin[Theta]Cos[Phi]

I want to plot the function Sin[Theta]Cos[Theta] in Mollweide map. I don't know how. Please help. Thank you so much!
2
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2answers
59 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. ...
4
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1answer
254 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^{...
5
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1answer
79 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, ...
13
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0answers
107 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
57 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: ...
2
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0answers
63 views

Elimination of trigonometric functions [closed]

I want to eliminate $\gamma$ from the system of equations given below: ...
7
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3answers
172 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 ...
0
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1answer
72 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, ...
0
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0answers
84 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 ...
1
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1answer
62 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 ...
2
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1answer
44 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
129 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
68 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
302 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 ...
2
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4answers
280 views

How to derive trigonometric Cartesian equation from parametric

How can one derive programmatically a Cartesian equation when $x$ and $y$ are parametrically represented by trigonometric functions? i.e.: Given that $x= \cos(2 t)$, and $y = -\sin(t)$, how can I ...
0
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2answers
48 views

FullSimplify not finding trig substitution with other terms present

Consider the following: FullSimplify[Cos[x - y - z] + Cos[x + y + z] + 1] Mathematica simply returns the exact expression with no simplification. However, if I ...
2
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1answer
38 views

Finding the 3D-model of a function that is rotated around the x-axis

How can I find the 3D model that is created by revolving the function: ...
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0answers
58 views

Convert Part of an Expression Using ExpToTrig

I'm wondering if there's a nice way to convert only parts of an expression, say exponential functions of varible $\theta$ to trig. The motivation is best descripbed by the following example. ...
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0answers
42 views

How to solve this trigonometric equation

The equation Sin[9 x - Pi/3] == Sin[7 x - Pi/3] can solved by hand Reduce[9 x - Pi/3 == 7 x - Pi/3 + k 2 Pi, x] x == ...
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2answers
81 views

How can I get solutions of this trigonometric equation?

I am trying to solve the equation $$\left(\sin (x)+\cos (x)-\sqrt{2}\right)\cdot \sqrt{-11 x-x^2-30}=0$$ in Real domain. I tried First way ...
2
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1answer
102 views

Combining ArcTan's like in Maple

It seems to me there is no simple way to combine ArcTan's with complex arguments symbolically in Mathematica as it is in Maple (https://www.maplesoft.com/support/help/Maple/view.aspx?path=combine%...
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0answers
41 views

Trigonometric derivation using Solve

Background: I'm trying to derive the relation between two variables in an optical system. The derivation is simple and well-known in the limiting case ($H \to \infty$, see figure), but rather tricky ...
1
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2answers
67 views

NSolve cannot find solution to system of trig equations

I was making a program to convert a rotation matrix to a set of euler angles. I wanted to do this for any valid rotation order that the euler angles were made with, and I did not want to do it the ...
0
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1answer
87 views

Complex Exponentials to Trig Functions?

I have an expression expr = 1/2 a E^(-3 I ω t) (E^(3 I ω t)+2 Cos[π x/a]) (1+2 E^(3 I ω t) Cos[π x/a]) Sin[π x/a]^2; expr // TeXForm $\frac{1}{2} a e^{-3 i t \...
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0answers
46 views

Different integration results when TrigToExp used

I am trying to do a double integral over a domain $x \in (\theta_1,\theta_2), y \in (0,\theta_1)$. Instead of doing a definite integral I am doing an indefinite integral and taking limits. All that is ...
-1
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2answers
118 views

How can I add two sin waves of different amplitude and frequency? [closed]

I've been tearing up the internet, but I can only find explanations for adding two sine waves of same amplitude and frequency, two sine waves of different amplitudes, or two sine waves of different ...
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0answers
39 views

Survey Question

Question for Civil Engineer or Surveyor I have a hypothetical question relative to the earth (sphere) and a square piece of land. If I buy a piece of land at the equator that is 1000 miles by 1000 ...
2
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2answers
135 views

FullSimplify a trigonometric expression doesn't work as expected

I know this kind of question is frequent asked, yet each case has its own particularities. I will show my problem. I define the following: ...
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1answer
38 views

Mathematica is not simplifying trignometric functions under Abs although I provide assumptions

I am trying to simplify a simple expression, (1/2)*((-Pi)*Abs[Sin[t]] - Pi*Abs[Sin[t - 2*Pi]] - 2*Pi*Abs[Sin[t - Pi]] + 4) i.e $$ \frac{1}{2} (-2 \pi \...
4
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1answer
97 views

How to convert Sine to Cosine?

I have some trigonometric quantities, which may be expressed in either sine or cosine, e.g., ia = Cos[wt], ib = -Sin[π/6 + wt], <...
2
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0answers
57 views

How to automatically transform Abs[Cos[x]]Sec[x] to Sign[Cos[x]]?

Out of some simplification, the term Abs[Cos[x]]Sec[x] appears. How can I make the code automatically transform ...
0
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1answer
68 views

Using constraints when solving a trigometric equation [closed]

I'm trying to learn how to add constraints/assumptions to equations when using Solve, sp as to avoid multi-valued solutions. For example, I'm trying to use ...
4
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1answer
66 views

Trouble with simplifying trigonometric / hyper-trigonometric functions

Why (correct) expressions like Assuming[p > 0, 2 ArcTan[Sinh[p]] == Pi - 2 ArcTan[Csch[p]] // FullSimplify] Are not correctly evaluated to: True? What is the ...
0
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1answer
28 views

Variable value is changing inexplicably [closed]

So I was trying to avoid doing some trig calculations on paper by using mathematica, when I encountered this (Screenshot in a new notebook, after having restarted everything): As you can see, B is ...
2
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1answer
108 views

Prevent simplification of trig functions

Mathematica often simplifies trigonometric expressions, for example replacing $\sin(\frac{\pi}{4})$ with $\frac{1}{\sqrt{2}}$, or replacing $\cos(\frac{3\pi}{8})$ with $\sin(\frac{\pi}{8})$. I'd like ...
7
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5answers
1k views

Fitting a Cos^2 function

I have to fit a Cos^2 function to data I measured. The function is $a \cos^2(\frac{bx\pi}{180}+c)+d $ and I tried the FindFit and Linear Model Function. I have 4 datasets which I have to fit, the ...

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