## Thomas' Calculus 13th Edition

$r=7 \sec \theta$
The conversion of polar coordinates and Cartesian coordinates are described as follows: 1. $r^2=x^2+y^2$ and $r=\sqrt {x^2+y^2}$ 2. $\tan \theta =\dfrac{y}{x} \implies \theta =\tan^{-1} (\dfrac{y}{x})$ 3. $x=r \cos \theta$ and 4. $y=r \sin \theta$ Given: $r \cos \theta=7$ This implies that $r=(7)(\dfrac{1}{\cos \theta})$ Hence, $r=7 \sec \theta$