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**vuze88** The hyperbolic spiral is given by the formula (in polar form), $\displaystyle r\theta=a$ for $\displaystyle \theta>0$ and some postive constant $\displaystyle a>0$. Use the fact that $\displaystyle \lim_{\theta\rightarrow 0}\frac{\sin\theta}{\theta}=1$ to prove there is a horizontal asympotote at $\displaystyle y=a$ and hence sketch the curve.

Basically, all i've done is a sketch of $\displaystyle r=\frac{a}{\theta}$ which isnt of great help. Ive also tried multiplying both sides by $\displaystyle \sin\theta$ to give $\displaystyle y=r\sin\theta=\frac{a\sin\theta}{\theta}$ but im unsure how complete the question and the sketch. Can someone give me some help please.