I have been asked to sketch the graph, from x = −5 to x = 5 of the odd function, $f(x)$, defined in the interval 0 < x < 5 by the formula $$f(x) ≡ \cos( πx/ 10)$$
The results I get are as follows :
However upon inspection of the correct graph mine is wrong. https://archive.uea.ac.uk/jtm/10/dg10p1.pdf
(Last page)
I have checked my results and can't see where it has gone wrong. any help is greatly appreciated, thank you.
It's a matter of English, not your mathematics. The question says:
$f$ is an odd function.
$f$ is defined to be the same as $\cos(\fracπ{10}x)$ on the interval $(0,5)$.
(1) tells you the rotational symmetry of the graph of $f$, and additionally tells you what $f(0)$ must be, which is not specified by (2). (2) tells you only what values $f$ takes on $(0,5)$, not including $0$ and $5$.
So there is a slight problem with the problem, that $f$ is not defined at $5$ and $-5$, but $f$ is indeed completely defined on the interval $(-5,5)$.