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 ...
- 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?
...
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 ...
- 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
- 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:
...
- 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 ...
- 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 ...
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
...
- 112k
14
votes
Accepted
Fitting a Cos^2 function
First, you better use NonlinearModelFit, Fit and FindFit haven't updated in a while, so ...
- 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:
...
- 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):
...
- 69k
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:
...
- 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)
...
- 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:
...
- 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:
...
- 14k
12
votes
Accepted
Mathematica 10 unable to Simplify[Cos[2 ArcCos[A]]]
Try TrigExpand
TrigExpand[Cos[2 ArcCos[A]]]
-1 + 2 A^2
- 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 ...
- 54.4k
11
votes
Solve symbolically a transcendental trigonometric equation and plot its solutions
Symbolically solve this equation:
...
- 14.2k
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:
...
- 220k
11
votes
Accepted
Simplifying a difficult trigonometric sum
Tan[(3 π)/11] + 4 Sin[(2 π)/11] // ToRadicals // FullSimplify
Sqrt[11]
- 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 ...
- 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 ...
- 64.6k
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 ...
- 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 ...
- 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 ...
- 124k
Only top scored, non community-wiki answers of a minimum length are eligible