Questions tagged [trigonometry]

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

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41
votes
3answers
12k views

How do I work with Root objects?

I want to solve the trigonometric equation : $$(3-\cos 4x )\cdot (\sin x - \cos x ) = 2.$$ I tried Solve[(3 - Cos[4*x])*(Sin[x] - Cos[x]) == 2, x] It returns the ...
17
votes
5answers
3k views

Solve symbolically a transcendental trigonometric equation and plot its solutions

I currently have the equation below for a beam with a hinge at various locations, the variable a can vary between 0 and 0.5. $$ Tan\left( {a\sqrt \alpha } \right) + Tan\left\{ {\left( {1 - a} \right)\...
21
votes
3answers
3k views

Mathematica Sec and Csc

How can I prevent Mathematica from using the "old fashioned" functions "Sec" and "Csc"? In Germany these functions are "old fashioned" as they are not taught anymore at school.
14
votes
3answers
4k views

Combining cosine or sine terms into a single cosine or sine

A function that is the sum of two cosine terms of the same frequency x[t_] := a1 Cos[w0 t + b1] + a2 Cos[w0 t + b2]; can be simplified to a single ...
3
votes
3answers
341 views

Speed up Eliminate

I have a set of trig equations, c1,c2,c3 are constants, I excepted the result is c1 c2 c3 r^2 + (c1^2 + c2^2 + c3^2 - 1) r + c1 c2 c3 == 0 but following code ...
30
votes
2answers
61k views

How to express trigonometric equation in terms of of given trigonometric function?

How can I express a trigonometric equation / identity in terms of a given trigonometric function? using following trigonometric identities ...
2
votes
4answers
5k views

Solve trigonometric equation

I'm looking for a solution (graphic, numeric or analytic) for a function of the form: $$a^2\tanh(x)=\tan(ax),\quad a ≥ 1,\ x > 0$$ preferably using Mathematica. Any advice?
6
votes
3answers
2k views

Replacing Tan[x] with Sin[x]/Cos[x]

Why doesn't this work? (1 - Tan[x])/(Sin[x] - Cos[x]) /. Tan[x] -> Sin[x]/Cos[x] I get back: ...
3
votes
3answers
6k views

Axes labels as multiples of $\pi$

I have a list as containing seven elements: ...
31
votes
1answer
29k views

Extract real part of a complex expression better than Re does

I have a complex expression with real positive variables only. Mathematica Input Style: ...
29
votes
4answers
6k views

How to find the period of an arbitrary mathematical function?

Is there a function to find the period of an arbitrary (possibly complex) function in Mathematica?
11
votes
4answers
6k views

Checking if two trigonometric expressions are equal

Say I have two trigonometric expressions which are a bit complicated. Is there a quick way to check if they reduce to the same thing (that they are equal) using Mathematica? I was solving this: $y'' ...
25
votes
1answer
828 views

Transform Root objects into Trigonometric expressions

Consider the Root objects roots = Table[Root[-1 + 27 #1^2 - 162 #1^4 + 243 #1^6 &, i],{i,1,6}] These can be expressed in terms trigonometric functions as ...
23
votes
3answers
4k views

Behavior of ArcTan when two zeros are given as arguments

I've noticed that the numeric approximation of ArcTan is a bit different from the symbolic one. If I write ArcTan[0,0] I ...
5
votes
4answers
412 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 /...
18
votes
4answers
709 views

How do I introduce a new variable in a trigonometric equation?

I have the trigonometric equation \begin{equation*} \sin^8 x + 2\cos^8 x -\dfrac{1}{2}\cos^2 2x + 4\sin^2 x= 0. \end{equation*} By putting $t = \cos 2x$, I have \begin{equation*} \dfrac{3}{16} t^4+ \...
11
votes
7answers
3k views

Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$

As an intermediate step, consider the function: f[x_] := x Sin[Pi/x] I want to prove that this function is increasing for $x\ge 1$. This can be done with the ...
0
votes
2answers
205 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 ...
14
votes
1answer
3k views

Simplify Sin[x]/x to Sinc[x]

I have an expression in the form of $\tt \frac{Sin[x]}{x}$ that I would like to simplify to the form of Sinc[x]. I've tried the ...
9
votes
2answers
7k views

How to expand tan(x+y) as normal form?

TrigExpand@Tan[x + y] gives $\frac{\sin (x) \cos (y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}+\frac{\cos (x) \sin(y)}{\cos (x) \cos (y)-\sin (x) \sin (y)}$ but I ...
2
votes
5answers
6k views

Solve simple trig equation

I would like to solve this equation: $$-x\sin(x)=\cos(x)$$ But Solve in Mathematica doesn't work: This system cannot be solved with the methods available to <...
18
votes
2answers
87k views

Generate a Unit Circle Trigonometry

Struggling often with Trigonometry I would like to have some code to generate this Unit Circle Trigonometry. Would be of great help when I need to transform some data :
17
votes
2answers
2k views

Why do certain values in ArcSin not fully evaluate?

This is a continuation of: Why do certain fractional values in TriangleWave not evaluate? The analysis by R.M and rasher revealed that problem to reduce to the behavior of: ...
11
votes
1answer
330 views

How does Mathematica calculate $\sin(\pi/5)$?

Consider: Sin[Pi/5] which returns: $$\sqrt{\frac58-\frac{\sqrt5}{8}}$$ Does anyone know how to figure out the trigonometric identities used by Mathematica to ...
10
votes
2answers
591 views

Evaluate trigonometric function

Can anyone help me to evaluate the trigonometric function below? Please look that the picture for more details. Here is the code to evaluate: ...
5
votes
4answers
303 views

How to compute the integral of trigonometic function with multiple angle

I got the following integral from a book and it is said that the integral should be zero within the domain $[-\pi, \pi]$ $$ \int_{-\pi}^{\pi}\sec(x)\cos[(m+1)(x+\pi/2)]\sin[m(x+\pi/2)]dx $$ where $...
5
votes
3answers
4k views

ArcTan[z] and ArcTan[x,y], Restriction and Conversion

In Mathematica there are two different forms for the arctangent (inverse tangent), namely ArcTan[x,y] which gives the arc tangent of $y/x$, taking into account ...
4
votes
1answer
492 views

How to solve this trigonometric system of equations numerically?

How can the following trigonometric system of equations be solved numerically? ...
9
votes
1answer
752 views

Need help on the proper use of a formula to produce a cambered airfoil

Following the book on "The Theory of Thin Wing Sections" page #112 describes the method to combine a camber line (i.e Mean Line) and a thickness distribution to form a cambered wing section. Data ...
2
votes
2answers
273 views

Showing steps for TrigExpand

If I enter a double equal sign and the following in Mathematica 10: == integrate 1/(1+x^4) Then wolfram alpha allows me to select a Step-by-step solution, which ...
0
votes
2answers
138 views

How can I put the results of TrigFactor function into a more convenient form?

a1 D11 Cos[n x] + a0 a1 D11 Cos[n x] + 1/2 a1 a3 D11 Cos[n x] + 1/2 a2 a4 D11 Cos[n x] I have a large trigonometric expression. Can I factor out different ...
-2
votes
1answer
1k views

Fitting data points using trigonometric functions [closed]

I want to curve fit some data points using a specific linear combination of trigonometric functions with the help of NonLinearModelfit as per the following code: ...
6
votes
2answers
419 views

Evaluating complicated trig without resorting to numerical methods

I have an angle theta given by Kx = (2/Sqrt[3]) ArcSin[Sqrt[3/10]]; Ky = (2/3) (ArcCos[(1/5) Sqrt[7/10]] - Pi); theta = Cos[ArcTan[Kx, Ky]]; This evaluates, by ...
5
votes
1answer
596 views

How to check if a given expression is an “explicit algebraic number”?

The documentation for PossibleZeroQ says: With the setting Method->"ExactAlgebraics"...
7
votes
2answers
268 views

Can I get Mathematica to recognize common series expansions of trigonometric functions?

I have some complicated functions from numerical procedures that go to simple trig functions in the limit of small time-steps. For example, I can calculate that one of these functions goes to: ...
7
votes
3answers
171 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 ...
5
votes
3answers
4k views

How to simplify 1 - Cos[2x] to 2 Sin[x]^2?

I want to reduce all Cos[2 x] to 1 - 2Sin[x]^2, it seems Mathematica will always simplify ...
2
votes
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: ...
2
votes
2answers
2k views

How to change the form $A\cos \omega t + B\sin \omega t$ into the form $\sqrt{A^2+B^2}\cos(\omega t-\phi)$ [duplicate]

I'm preparing notes for teaching next week's class in differential equations. My hand calculation solution of $$y''+192y=0, y(0)=1/6, y'(0)=-1$$ is $$y=\frac16\cos 8\sqrt3 t-\frac{\sqrt3}{24}\sin 8\...
0
votes
2answers
2k views

Avoid trigonometric simplifications?

When evaluating the expression Sinh[x]^2 + Cosh[x]^2 // FullSimplify I get Cosh[2 x] That is indeed a simplification, but ...
9
votes
4answers
595 views

How to make Mathematica simplify $\cos[(i + j + k)\pi]$ to $(-1)^{i+j+k}$?

We know that: $$ \cos\left[(i+j+k)\pi\right] = (-1)^{i+j+k} $$ for $i, j, k$ being positive integers. In Mathematica I've tried: ...
7
votes
1answer
298 views

Quantity and Trig functions

I have a bunch of data to which I've assigned units using Quantity, including some angular measurements in degrees. I'd like to be able to use these measurements ...
3
votes
3answers
901 views

How to extract phase angle from sinusoid

I'm doing some electric circuit calcualtions and I'm trying to get the phasor representation of some arbitrary function of Sin or Cos. Could be complex like: ...
3
votes
1answer
248 views

Simplifying a trigonometric function with arctan

Why is this trigonometric expression with $\arctan$ not simplified ? ArcTan[Tan[γ[t] - θ[t]]]
3
votes
3answers
117 views

Solve command returns duplicate answers

Mathematica 11.0.1. In the documentation for the Solve command: When a single variable is specified and a particular root of an equation has multiplicity greater than one, Solve gives several copies ...
3
votes
2answers
207 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 ...
3
votes
3answers
295 views

Integral of trigonometric function gives different answer [duplicate]

I am working on an integral on the following trigonometric functions $$\int_{-\pi}^\pi \frac{\cos[(4m+2)x] \cos[(4m+1)x]}{\cos x}dx$$ where $m$ is positive integer. I am running the following code ...
2
votes
3answers
1k views

DSolve will not apply assumption m ∈ Integers

I am trying to solve a linear second order ODE using DSolve which involves an arbitrary integer m. ...
2
votes
1answer
997 views

Solve[Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] breaks when “Reals” is added?

Mathematica solves this equation fine: Solve[ Tan[theta] == (b*Sin[t])/(a*Cos[t]), theta] // InputForm ...
2
votes
0answers
98 views

TrigExpand Idiosyncracies

TrigExpand[Sin[x]^2 Log[y]] returns sin^2(x) log(y), as one would expect. However, ...