[SOLVED] Parametric Representation of a Curve

Hey,

Find the equation in $\displaystyle x$ and $\displaystyle y$ for the curve given parametrically

by $\displaystyle x = sec(t) $ and $\displaystyle y = tan(t)$, where $\displaystyle \frac{-\pi}{2} < t < \frac{\pi}{2}$. What type of

curve is it?

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So I've written that $\displaystyle x = \frac{1}{cos(t)}$ and $\displaystyle y = \frac{sin(t)}{cos(t)}$.

From that $\displaystyle t= cos^{-1} \frac{1}{x}$

If I substitute that in $\displaystyle y = \frac{sin (cos^{-1} \frac{1}{x})}{\frac{1}{x}}$.

But that's where I get stuck..I'm not sure if I've even started correctly. What do you with the fact they've told you that $\displaystyle \frac{-\pi}{2} < t < \frac{\pi}{2}$?

Any help would be greatly appreciated!!