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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 :enter image description here

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.

ForgotALot
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Aztec warrior
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    yours is correct for $\cos ( \pi x / 10$ for all $x$ from $-5$ to $5.$ However, they wanted the odd extension of the part from $0$ to $5.$ This means you take the indicated part, $x > 0,$ and rotate that $180^\circ$ around the origin and draw that in. – Will Jagy May 04 '16 at 01:25
  • It says "for the odd function...cosine" But, cosine is an even function, not an odd function, so something is definitely wrong with the example. Perhaps the author intended to use a different example and typed the wrong function. – JMoravitz May 04 '16 at 01:30
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    @WillJagy : Is there a reason your answer is not an Answer? – Eric Towers May 04 '16 at 01:31

1 Answers1

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It's a matter of English, not your mathematics. The question says:

  1. $f$ is an odd function.

  2. $f$ 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 $(-5,5)$.

user21820
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