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 ...
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 ...
Community wiki
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?
...
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 ...
22
votes
How to make mathematica give 1/0 as infinity
Use the two-arg version of ArcTan instead:
ArcTan[0, 4]
π/2
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:
...
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 ...
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 ...
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->-...
Community wiki
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
...
14
votes
Accepted
Fitting a Cos^2 function
First, you better use NonlinearModelFit, Fit and FindFit haven't updated in a while, so ...
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:
...
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):
...
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:
...
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)
...
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.
Community wiki
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:
...
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:
...
12
votes
Accepted
Mathematica 10 unable to Simplify[Cos[2 ArcCos[A]]]
Try TrigExpand
TrigExpand[Cos[2 ArcCos[A]]]
-1 + 2 A^2
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 ...
11
votes
Solve symbolically a transcendental trigonometric equation and plot its solutions
Symbolically solve this equation:
...
11
votes
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:
...
11
votes
Accepted
Simplifying a difficult trigonometric sum
Tan[(3 π)/11] + 4 Sin[(2 π)/11] // ToRadicals // FullSimplify
Sqrt[11]
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 ...
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 ...
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 ...
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 ...
10
votes
Accepted
Expand wedge product
One idea is to use TensorReduce. I will assume that r is real, and that Dt[r] and ...
Only top scored, non community-wiki answers of a minimum length are eligible
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