Question

find the rectangular form of the curve give by; x=sec theta and y=tan theta

Answer 1

\[\arctan(\tan\theta)=\arctan(y)=\theta\]

Answer 2

\[\tan \theta=\frac{\cos\theta}{\sin \theta} \\
\sec \theta=\frac1 {\cos \theta}\\
\sec^2\theta=\pm( 1-\tan^2 \theta)\\
x=\pm \sqrt{1 - \tan^2(\arctan y)}\\
x=\pm \sqrt{1 - y^2}\\
y= \pm \sqrt{1-x^2}\\\]
That last one should be the answer.