28 votes
Accepted

Solve symbolically a transcendental trigonometric equation and plot its solutions

General remarks These are are crucial aspects of solving equations symbolically: So far (in general) Mathematica cannot solve transcendental equations when two unknowns are involved, nevervetheless ...
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  • 54.4k
26 votes

How do I work with Root objects?

This answer is to summarize the most important points about working with Root objects. Essential reading: Algebraic Numbers in the documentation. What are ...
23 votes

Why does Mathematica give this ArcSin[2] result?

I. $\sqrt{z}$ Quick, what's the square root of $4$? If you said $2$, you're right! If you said $-2$, you're right! Wait, what? ...
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22 votes
Accepted

Transform Root objects into Trigonometric expressions

Disclaimer: This is not a full answer, but perhaps it's a start. From an algebraic stand point this seems like a very hard problem. I attacked it with a more brute force approach. I guess a basis and ...
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  • 33.2k
22 votes

How to make mathematica give 1/0 as infinity

Use the two-arg version of ArcTan instead: ArcTan[0, 4] π/2
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  • 124k
21 votes

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

Mathematica auto simplifies simple trig expressions like these, but you can turn off this setting via SystemOptions: ...
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  • 33.2k
17 votes
Accepted

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

I have to thank you for leading me down a fascinating rabbit hole! I have always found airfoil shapes enormously pleasing, but I was not aware of the NACA system. For those who, like me, did not know ...
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  • 61.6k
16 votes

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

In the course of answering this question, I ran into a little bit of weirdness that doesn't square with my experience with previous versions of Mathematica. I think writing this answer is as good a ...
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15 votes
Accepted

Solve simple trig equation

Restrict the domain: Solve[-x Sin[x]==Cos[x]&&-30<=x<=30,x,Reals]//N {{x->-28.2389},{x->-25.0929},{x->-21.9456},{x->-18.7964},{x->-15.6441},{x->-...
15 votes
Accepted

Evaluate trigonometric function

We know that FullSimplify[ArcTan[k] + ArcTan[1/k], k > 0] does not do it. But by first converting to exponentials, now Mathematica does it ...
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  • 112k
14 votes
Accepted

Fitting a Cos^2 function

First, you better use NonlinearModelFit, Fit and FindFit haven't updated in a while, so ...
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  • 3,817
14 votes
Accepted

How to draw a phasor animation with Mathematica?

Trying to do this with plots may end up being very difficult. I tend to use the plot as a base and then add ancillary graphics around it, e.g. with Show: ...
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  • 61.6k
14 votes
Accepted

Why does Mathematica not give the simple solution of the given equations?

I think your assumption is that $y\in \mathbb{R}$ is real, so you can put it as the condition (otherwise it is assumed to be complex): ...
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13 votes

Axes labels as multiples of $\pi$

I found the solution I was looking for at https://stackoverflow.com/questions/8936579/labeling-a-plot-in-increments-of-pi. example: ...
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  • 233
13 votes
Accepted

Simplify $\tan(\arctan(a) - \arctan(b))$

Here's two possibilities: Simplify[TrigExpand[Tan[ArcTan[a] - ArcTan[b]]]] (a - b)/(1 + a b) ...
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  • 33.2k
13 votes
Accepted

How can I make Mathematica do, ArcTanh[x] + ArcTanh[y] = ArcTanh[x+y/1+xy]?

A little bit of trickery: ArcTanh[x] + ArcTanh[y] // Tanh // TrigExpand // FullSimplify // ArcTanh (* ArcTanh[(x + y)/(1 + x y)] *) Note the parentheses.
13 votes
Accepted

Mathematica in degrees mode

Possibly a bad idea for the reasons mentioned in previous messages, but you could do something like the following: ...
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  • 10.6k
12 votes
Accepted

Eliminate 3 Variable from 4 Equations

Removing the double angles (e.g. $\cos(2 \theta) = \cos^2(\theta) - \sin^2(\theta)$) with TrigExpand allows the elimination to be performed: ...
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  • 14k
12 votes
Accepted

Mathematica 10 unable to Simplify[Cos[2 ArcCos[A]]]

Try TrigExpand TrigExpand[Cos[2 ArcCos[A]]] -1 + 2 A^2
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  • 32.5k
12 votes

How to solve this system of trigonometric trancendental equations over the reals?

Sin is defined in the whole complex plane, while ArcSin is not. Solving a system involving ...
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  • 54.4k
11 votes

Solve symbolically a transcendental trigonometric equation and plot its solutions

Symbolically solve this equation: ...
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  • 14.2k
11 votes

Amplitude of a Sinus, Simple question

One way is to use Interval. ...
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  • 220k
11 votes
Accepted

Computing the seven roots of a polynomial

poly = x^7 + x^6 - 18 x^5 - 35 x^4 + 38 x^3 + 104 x^2 + 7 x - 49; Find an extension in which the polynomial splits: ...
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  • 220k
11 votes
Accepted

Simplifying a difficult trigonometric sum

Tan[(3 π)/11] + 4 Sin[(2 π)/11] // ToRadicals // FullSimplify Sqrt[11]
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  • 35.9k
11 votes
Accepted

Why doesn't Mathematica know the exact value of some trivial trigonometric functions?

An answer to How does Mathematica calculate $\sin(\pi/5)$? by @J.M. points out that in the Notes on Internal Implementation, it is implied that FunctionExpand is ...
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  • 220k
10 votes

Mathematica Sec and Csc

Using the neat trick Chip showed in this answer: ...
10 votes
Accepted

Sum to Product Trig Identities

As the TrigFactor help page says under Possible issues: A trigonometric expression can be factored in many different ways Looking at the Wikipedia page of ...
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10 votes

Evaluate trigonometric function

This works: Assuming[k > 0, Solve[FullSimplify[ArcTan[k] + ArcTan[1/k] == x], x]] (* ==> {{x -> Pi/2}} *) Here, I equate the expression in the ...
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  • 95.3k
10 votes
Accepted

Convert radian to degree and add °

I resolved that using (Pi/4) * (180 Degree /Pi) Degree is a symbol similar to Pi, it ...
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  • 495
10 votes
Accepted

Expand wedge product

One idea is to use TensorReduce. I will assume that r is real, and that Dt[r] and ...
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  • 124k

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