Questions tagged [trigonometry]

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

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votes
4answers
242 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
39 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
32 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
45 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
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0answers
39 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
75 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
74 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
39 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
35 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
40 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
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0answers
43 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
86 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
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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
121 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
33 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
81 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
51 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
56 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 ...
3
votes
0answers
33 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
69 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
169 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
668 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:...
6
votes
1answer
77 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
64 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}...
3
votes
4answers
245 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
11
votes
3answers
288 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
56 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
138 views

How to solve this trigonometric integral analytically

I'm trying to solve the following integral analytically : ...
0
votes
1answer
103 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
228 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}]
0
votes
1answer
135 views

I need to solve this equation: 2 cos^2 θ − 7 cos θ − 4 = 0 on the interval 0 ≤ θ < 2 π [closed]

I've been trying to solve the problem, but I keep getting errors.Thanks for the help.
1
vote
1answer
48 views

Solve command doesn't work (i'm beginner)

I try to perform the equation by writing: ...
0
votes
1answer
68 views

Interpretation of PolarPlot

I tried to plot the function $r=-2t$ with $t$ in $[0,2\pi]$: PolarPlot[-2 t, {t, 0, 2 Pi}, AxesLabel -> {x, y}] When $t=\pi/4$, I have: $$r=-\pi/2=-1.57$$ ...
0
votes
1answer
68 views

FullSimplify not simplifying expression containing the form Sin[n] where n is an integer [closed]

I have a function f[n] which give 0 for integer input, but FullSimplify doesn't work for it, why? ...
3
votes
1answer
61 views

Generating trigonometric sums

How can one generate all cosine polynomials with $\pm1$ coefficient of following form: $$\sum_{k=1}^n\pm\cos kt.$$ I tried DO loop but couldn't get all of them as clearly cannot exhaust $2^n$ ...
2
votes
1answer
116 views

Domain and codomain of a function

I am wondering if it is possible to get domain and codomain of a function in Mathematica (by using only built-in functions if possible). For example, I would like to give as input the function $tan(x)$...
4
votes
4answers
284 views

Alternative form of ArcSin[Sin[x]]

Is it possible to get the following result in Mathematica by using only built-in functions: $$\arcsin( \sin(x)) = x $$ if $x \in [-\pi /2 , \pi/2]$ $$\arcsin ( \sin(x)) = \pi - x $$ if $x \in [\pi /...
3
votes
1answer
75 views

Given two lines find the four circles that have the lines as tangents

Given two lines, each defined by two points, and a radius find the four circles that have the lines as tangents. I give my attempt below but there ought to be a nice mathematica way of doing this. <...
0
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0answers
43 views

Finding the functions that Mathematica plots while using BodePlot

I've the following Mathematica-code: ...
2
votes
2answers
150 views

Fourier Phase Angle Interpretation

I am trying to fit the following tide data (taken from here) with a sinusoidal curve that looks like the following: displacement+amplitude * sin(t w - ph), where t is the independent variable, w is ...
1
vote
1answer
52 views

Plot contour of zeroes against trig function

Take two functions: func1=Cos[Pi*x]*Cos[Pi*y] func2=x Sin[Pi*x] I want to create a plot that shows a 2D contour map of ...
1
vote
1answer
42 views

Strange output for solve in terms of trigonometric functions

I am using the following Solve code: ...
0
votes
1answer
65 views

Defined function doesn't plot correctly

I have defined a function that produces a single negative impulse spanning -b to -a and a positive impulse spanning ...
1
vote
1answer
73 views

Plot of integral of summed `Sinc` series is incorrect

I have curve given by summing a small, finite series of Sinc functions, and I want to plot both the curve and its integral. In principle, it's easy: ...
0
votes
1answer
67 views

Incorrect results in trig table

I have a table given by Table[ Evaluate[ Sum[(Sin[(2 π j x)/(r + 1)])/(r + 1), {j, 0, r}]], {r, 1, 25}, {x, 0, 25}] /. Indeterminate -> 0 The ...
1
vote
1answer
43 views

Find closed form for roots of trig formula

I have the expression Sum[(2 j \[Pi] Sin[(2 j \[Pi] x)/(r + 1)])/(r + 1)^2, {j, 0, r}] == 0 I want to find the roots in terms of ...
3
votes
2answers
102 views

Indefinite ArcTan integral does not return the (known) real expression but returns complex expression

I have a problem with an indefinite integral which I solved using MMA in back in 2010 (must have been version 7 or 8) successfullly and it gave an elegant result. However, if I run it with MMA 11.3 (...
3
votes
1answer
126 views

Indeterminate result from Sinc

I have an impulse train given by (1 + Csc[(π x)/(1 + R)] Sin[(π (1 + 2 R) x)/(1 + R)])/(2 + 2 R) Because of the Csc, ...