Taylor polynomial/1 over sine/pi over 2/Exercise

We consider the function

${}f(x)={\frac {1}{\sin x}}\,$

over the real numbers.

a) Determine the range of ${}f$.

b) Sketch ${}f$ for ${}x$ between ${}-2\pi$ and ${}2\pi$.

c) Determine the first three derivatives of ${}f$.

d) Determine the Taylor-polynomial of order ${}3$ of ${}f$ in the point ${}{\frac {\pi }{2}}$.

Create a solution