Questions tagged [trigonometry]
Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.
535 questions
2 votes
1 answer
110 views
Integration of function involving ArcCsc with assumptions returns wrong answer
When I ask Mathematica (version 14.1) to do the following symbolic integration: ...
- 1,073
2 votes
4 answers
198 views
Trigonometric Simplification
I do not understand why a simple trigonometric expression is not simplified even when I supply a reduced domain of the variable. More precisely, I do not understand why ...
1 vote
1 answer
305 views
How can I evaluate limit of ArcTanh with complex Tan as argument? [closed]
How can I evaluate this limit? Limit[ArcTanh[((-5 + I Sqrt[23]) Tan[x/2])/Sqrt[58 - 2 I Sqrt[23]]], x -> π] Mathematica returns Indeterminate. The expected ...
- 1,758
2 votes
1 answer
183 views
FindInstance has difficulty computing more than one solution to a certain type of trigonometric inequality
FindInstance has difficulty computing more than one solution to this type of trigonometric inequality: $$\arccos(\cos(\theta_1 - \theta_2)) + \arccos(\cos(\theta_2 -...
- 2,665
2 votes
1 answer
188 views
How can I simplify $\tan(\pi/9)-\tan(2\pi/9)+\tan(4\pi/9)$ to $3\sqrt3$?
The following equality is not immediately confirmed by Mathematica: (Engine 14.1.0) Tan[Pi/9]-Tan[2Pi/9]+Tan[4Pi/9] == 3Sqrt[3] (* Echoes back the expression! *) ...
- 381
0 votes
0 answers
98 views
Matrix Equality
Let $$g = \begin{pmatrix} \cos{r}+\frac{i\theta_3}{2r}\sin{r} & \frac{i\theta_+}{r}\sin{r}\\ \frac{i\theta_-}{r}\sin{r}& \cos{r}-\frac{i\theta_3}{2r}\sin{r} \end{pmatrix},$$ where $r = \frac{1}...
9 votes
7 answers
901 views
Simplifying a trigonometric expression involving ArcTan
I have the following formula expr = 2 ArcCsc[r] + 7 ArcTan[Sqrt[-1 + r^2]] + 10 ArcTan[r - Sqrt[-1 + r^2]] I have seen plotting it or also assigning different ...
- 543
4 votes
1 answer
307 views
Equality test of two hyperbolic expressions
I am trying to compare two expressions to see whether they are equal using approximations: $$\coth \left(\frac{\pi }{4}\right)+\frac{1}{2} \text{csch}^2\left(\frac{\pi }{4}\right),$$ $$\sum _{k=1}^{\...
- 277