Questions tagged [trigonometry]

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

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2
votes
2answers
61 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\...
5
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2answers
75 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
votes
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?
0
votes
0answers
54 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
votes
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
votes
1answer
247 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
votes
1answer
77 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
104 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
votes
1answer
56 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
59 views

Elimination of trigonometric functions [closed]

I want to eliminate $\gamma$ from the system of equations given below: ...
7
votes
3answers
168 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
votes
1answer
70 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
82 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
vote
1answer
58 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
votes
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 ...
3
votes
2answers
125 views

Solar Power Calculations

Good Afternoon, I have calculated the Incident beam radiation for a given locations local sunlight hours. ...
0
votes
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
votes
1answer
297 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
votes
4answers
276 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
votes
2answers
47 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
votes
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: ...
0
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0answers
53 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. ...
0
votes
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 == ...
1
vote
2answers
79 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
votes
1answer
98 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%...
0
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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
vote
2answers
58 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
votes
1answer
71 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 \...
0
votes
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
votes
2answers
105 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 ...
0
votes
0answers
38 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
votes
2answers
132 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: ...
1
vote
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
votes
1answer
92 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
votes
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
votes
1answer
64 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
votes
1answer
65 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
votes
1answer
27 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
votes
1answer
93 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
votes
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 ...
5
votes
4answers
191 views

Simplify $\tan^{-1}(\cot(a))$ to $\frac{\pi }{2}-a$ assuming $0<a<\frac{\pi }{2}$

I know Mathematica is not omnipotent, but still can't help feeling surprised when I encountered this example, and I think it's worth starting a question for it. The example is, ...
4
votes
2answers
673 views

Mathematica gives an unexpected answer for Integrate [closed]

I need to integrate the following: \begin{equation}\tag{1} \frac{\sqrt{C + (1 - C) x^3}}{x}, \end{equation} where $0 < C < 1$ and $x$ is a positive variable (then $x^3 \ge 0$). When I integrate:...
8
votes
2answers
131 views

Computing the seven roots of a polynomial

This question was originally asked by @fsrong70 six months ago. The OP deleted it shortly after posting and has not returned to this site since. I had just figured it out when it was deleted. I ...
3
votes
1answer
76 views

Simplifying symbolic integration with trigonometric functions

I am using DSolve to verify a multitude of definite integrals I have done by hand, and things have gone perfectly until this integral, $$ \int_0^t \frac{\mathrm{d}...
4
votes
4answers
390 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
11
votes
3answers
309 views

Simplifying Cosh[a] + Sin[a] + Sinh[a]

Why does FullSimplify[Cosh[a] + Sinh[a] + Sin[a]] not return Exp[a]+Sin[a] ? Is this some bug in Mathematica or am I being ...
0
votes
1answer
76 views

Different solution on trigonometric function in mathematica and wolframalpha using Simplify and FullSimplify [closed]

I have this expresion: -cos(a3) (cos(a2) sin(a1) + cos(a1) sin(a2)) And when I simplify with wolframalpha online, it give me this: ...
1
vote
1answer
140 views

How to solve this trigonometric integral analytically

I'm trying to solve the following integral analytically : ...
0
votes
1answer
181 views

Blood Pressure problem given equation [closed]

The blood pressure (P) of an individual after t seconds with a heart rate of 70 beats/min. can be modeled by the function, P(t) = 100 + 20 sin(7π/3)t In the time interval from 0s ...
0
votes
1answer
278 views

Trouble plotting P(t) = 100 + 20 sin(7π t/3) [closed]

I'm trying to plot this but I keep getting an empty graph. I put in: Plot[P[t_] := 100 + 20 sin[(7 pi)/3] t, {t, 0, 10}]

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