Questions on trigonometric and hyperbolic functions, as well as their inverses, in Mathematica.
4
votes
2answers
617 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 ...
7
votes
1answer
2k 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:
...
11
votes
1answer
4k 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
...
6
votes
5answers
559 views
Trying to prove that $x\sin(\frac{\pi}{x})\ge\pi \cos(\frac{\pi}{x})$ for $x\ge 1$
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 first derivative. We have to ...
7
votes
2answers
672 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 ...
16
votes
4answers
415 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+ ...
8
votes
2answers
5k 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 :
0
votes
2answers
141 views
Simplifying a trigonometric equation to obtain specific terms
When I try to solve the non-homogeneous differential equation
...
