Tagged Questions
5
votes
4answers
379 views
How to transform the result of this integral into powers of $\sin\,x$?
I want to calculate the integral
$I = \displaystyle\int{\cos ^5 x\, \mathrm dx}$. Using the variable $t = \sin x$, I get
$$I = \sin x - \frac{2}{3}\sin^3 x + \frac{1}{5}\sin^5 x + C.$$
With ...
0
votes
2answers
124 views
Sum of roots of a trigonometric equation
The equation $$ \sin x + \sqrt{3} \cos x = 1,$$
where $x \in [-2\pi, 2\pi]$ has four roots $-\dfrac{3\pi}{2}$, $\dfrac{\pi}{2}$, $\dfrac{\pi}{2}$ and $\dfrac{11\pi}{6}$. Sum of roots of the given ...
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+ ...
9
votes
2answers
310 views
Mathematica Sec and Csc
How can I prevent Mathematica from using the "old fashioned" functions "Sec" and "Csc"?
In Germany these functions are "old fashioned" as they are not taught anymore at school.
4
votes
2answers
564 views
ArcTan expressed as a radian fraction?
This type of answer is what I'm looking for:
In[58]:= ArcTan @ 1
Out[58]= π/4
This is what mathematica gives me:
...
