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More specifically, how would you write $\csc(-2\pi/5)$ as the trigonometric function of a positive number?

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sine (and hence cosecant) is an odd function. Basically, you can take the negative outside. – The Chaz 2.0 Apr 25 '12 at 1:42
Just to clarify what Chaz is saying, $$\sin(-x) = -\sin x$$ from where the same holds for the cosecant. – Pedro Tamaroff Apr 25 '12 at 1:47
up vote 1 down vote accepted

Hint: Recall that $\sin(x)=\sin(x+2k\pi)$ for any integer $k$. Let $x=-2\pi/5$ and let $k=1$.

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This might be more in line with the desired solution than my comment above, but who knows! "This answer is useful" – The Chaz 2.0 Apr 25 '12 at 2:20

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