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Questions tagged [trigonometry]

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

1
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1answer
26 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
78 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], <...
0
votes
0answers
10 views

Trigonometry equation that includes two sin and a con [migrated]

How would I arrange this equation (3sin2x=5sin2xcos2x) to get either cos sin or tan by itself? I’ve tried to do the sin/cos to get tan, but I’m unsure how to get the second sin in terms of tan or if ...
2
votes
0answers
49 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
51 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
31 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
58 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
154 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
664 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
72 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
61 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
197 views

Continuous non-piecewise equivalent of smoothstep function?

I have a smooth step function given by the piecewise function ...
11
votes
3answers
269 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
49 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
136 views

How to solve this trigonometric integral analytically

I'm trying to solve the following integral analytically : ...
0
votes
1answer
91 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
179 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
94 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
45 views

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

I try to perform the equation by writing: ...
0
votes
1answer
66 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
61 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
60 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
102 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
261 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
71 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
votes
0answers
39 views
2
votes
2answers
140 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
48 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
41 views

Strange output for solve in terms of trigonometric functions

I am using the following Solve code: ...
0
votes
1answer
62 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
70 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
41 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
94 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
123 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, ...
4
votes
1answer
79 views

Solve/Reduce not working on a function with a condition/domain restriction?

I'm working with a trigonometric function, so I thought it would be convenient to set a condition to restrict the domain so I wouldn't have to specify it in the solve function each time. Here is a ...
4
votes
1answer
100 views

Prevent Trigonometric simplifications from using double angle and half angle formulae?

Is there any way to force Mathematica to not use double and half angle formulae etc. when simplifying Trigonometric expressions? For example,...
2
votes
1answer
107 views

Convert trigonometric expression into other forms using just a specific set of identities

I am trying to convert a trigonometric expression like sinθ/(1 - cosθ) into cosecθ + cotθ or ...
1
vote
1answer
71 views

Why is this function indeterminate?

Consider an impulse train 1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1) For x=0 it's clear that this function ...
0
votes
2answers
114 views

How can I avoid the message Infinity::indet?

I have an impulse train of frequency R: 1/(R + 1) + (Sum[Cos[(2 k π x)/(R + 1)], {k, R}])/(R + 1) For ...
0
votes
2answers
37 views

Force a result from “Indeterminate” for single impulse?

The formula for a single impulse of amplitude $1$ at $x=r$ is given by $$\frac {\sin (\pi (x-r))}{\pi (x-r)}$$ (In MathJax because it's a math formula.) Formally, at $x=r$, this function evaluates ...
1
vote
1answer
30 views

Trigonometric simplification with assumptions fails

Consider the following input Assuming[Element[y, Integers], (-1 + E^(I \[Pi] (x + y)))/(-1 + E^(I \[Pi] (x - y)))//FullSimplify] ...
0
votes
2answers
46 views

Plotting a function while varying a variable (on the x-axis) using two formulas [duplicate]

I want to plot the following function, where Rb is the variable (that has to be on the x-axis): ...
6
votes
1answer
262 views

Integral that yields ArcTan function rather than ArcSin

When I enter the following Integral problem to Mathematica, $$ \int \frac{1}{\sqrt{a²-x²}}\textrm{d}x $$ The answer yielded by Mathematica is $$ \arctan\left({\frac{x}{\sqrt{a²-x^2}}}\right) $$ Rather ...
1
vote
1answer
43 views

Not getting expected simplification of trigonometric expressions

I have two trigonometric expressions. I would like to eliminate the fraction from my 2nd expression. ...
1
vote
2answers
111 views

Solve trig equation

I have a simple trig equation: Clear[f, x] f[x_] = Cos[2*x] - 3 Sin[x] + 2 Solve[f[x] == 0, x] I received a very long a complicated reply that I do not ...
0
votes
1answer
89 views

Get the square root of a+bi,when a>0,b>0 in radical form

My code returns this result involves trigonometric functions, ...